matlab解非线性方程组？

用Solve（）函数可求解此非线性超越方程组，得到解析解。
syms th1 th2 th3 th4
syms r1 r2 r3 r4
s=solve(r2*cos(th2)+r3*cos(th3)-r1-r4*cos(th4),r2*sin(th2)+r3*sin(th3)-r4*sin(th4),'th3,th4')
s =
th3: [2x1 sym]
th4: [2x1 sym]
s.th3 =
atan(-(r2*sin(th2)-1/2/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)+4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2)))/r3,1/2*(r2*sin(th2)/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)+4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2))-2*r2^2*sin(th2)^2+r3^2-2*r2*cos(th2)*r1+r1^2-r4^2+r2^2)/r3/(-r2*cos(th2)+r1))
atan(-(r2*sin(th2)-1/2/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)-4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2)))/r3,1/2*(r2*sin(th2)/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)-4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2))-2*r2^2*sin(th2)^2+r3^2-2*r2*cos(th2)*r1+r1^2-r4^2+r2^2)/r3/(-r2*cos(th2)+r1))
s.th4 =
atan(1/2/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)+4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2))/r4,-1/2*(r2^2-2*r2*cos(th2)*r1-r2*sin(th2)/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)+4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2))-r3^2+r1^2+r4^2)/(-r2*cos(th2)+r1)/r4)
atan(1/2/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)-4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2))/r4,-1/2*(r2^2-2*r2*cos(th2)*r1-r2*sin(th2)/(-8*r2*cos(th2)*r1+4*r1^2+4*r2^2)*(4*r2*sin(th2)*r4^2-8*r2^2*sin(th2)*cos(th2)*r1-4*r2*sin(th2)*r3^2+4*r2*sin(th2)*r1^2+4*r2^3*sin(th2)-4*(6*r2^4*sin(th2)^2*r1^2-r3^4*r2^2-8*r2*cos(th2)*r1^3*r3^2+r2^2*sin(th2)^2*r4^4-r1^2*r4^4+8*r2^2*cos(th2)^2*r1^2*r3^2-2*r2^4*sin(th2)^2*r3^2+2*r3^2*r1^4+2*r2*cos(th2)*r1*r3^4-2*r2^4*sin(th2)^2*r4^2-7*r1^2*r2^4+2*r1^4*r4^2-7*r1^4*r2^2-r3^4*r1^2-8*r2^3*cos(th2)*r1*r3^2+r2^2*sin(th2)^2*r3^4+2*r2*cos(th2)*r1*r4^4+5*r2^2*sin(th2)^2*r1^4-4*r2*cos(th2)*r1*r3^2*r4^2+r2^6*sin(th2)^2+4*r2^3*sin(th2)^2*r4^2*cos(th2)*r1+2*r3^2*r1^2*r4^2+4*r3^2*r1^2*r2^2+2*r3^2*r4^2*r2^2+2*r3^2*r2^4-2*r2^2*sin(th2)^2*r4^2*r3^2-2*r2^2*sin(th2)^2*r4^2*r1^2+4*r2^4*sin(th2)^2*cos(th2)^2*r1^2-12*r2^3*sin(th2)^2*cos(th2)*r1^3-4*r2^5*sin(th2)^2*cos(th2)*r1-2*r2^2*sin(th2)^2*r3^2*r1^2+8*r2^2*cos(th2)^2*r1^2*r4^2-r1^6-r2^6-r2^2*r4^4+4*r1^2*r4^2*r2^2+20*r2^3*cos(th2)*r1^3-8*r2^2*cos(th2)^2*r1^4-8*r2^4*cos(th2)^2*r1^2+6*r2*cos(th2)*r1^5+6*r2^5*cos(th2)*r1+2*r2^4*r4^2-8*r2*cos(th2)*r1^3*r4^2-8*r2^3*cos(th2)*r1*r4^2+4*r2^3*sin(th2)^2*cos(th2)*r1*r3^2)^(1/2))-r3^2+r1^2+r4^2)/(-r2*cos(th2)+r1)/r4)

>> equ1=sym('R2*cos(th2)+r3*cos(th3)-r1-r4*cos(th4)=0');
>> equ2=sym('R2*sin(th2)+r3*sin(th3)-r4*sin(th4)=0');
>> S=solve(equ1,equ2,'th3','th4');
>> S.th3

ans =

atan(-(R2*sin(th2)-1/2/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2+4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2)))/r3,1/2*(-R2*sin(th2)/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2+4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2))+2*R2*cos(th2)*r1-r1^2+r4^2+2*R2^2*sin(th2)^2-R2^2-r3^2)/r3/(-r1+R2*cos(th2)))
atan(-(R2*sin(th2)-1/2/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2-4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2)))/r3,1/2*(-R2*sin(th2)/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2-4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2))+2*R2*cos(th2)*r1-r1^2+r4^2+2*R2^2*sin(th2)^2-R2^2-r3^2)/r3/(-r1+R2*cos(th2)))

>> S.th4

ans =

atan(1/2/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2+4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2))/r4,-1/2*(2*R2*cos(th2)*r1-R2^2+R2*sin(th2)/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2+4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2))-r1^2-r4^2+r3^2)/(-r1+R2*cos(th2))/r4)
atan(1/2/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2-4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2))/r4,-1/2*(2*R2*cos(th2)*r1-R2^2+R2*sin(th2)/(8*R2*cos(th2)*r1-4*r1^2-4*R2^2)*(-4*R2*sin(th2)*r4^2-4*R2^3*sin(th2)-4*R2*sin(th2)*r1^2+8*R2^2*sin(th2)*cos(th2)*r1+4*R2*sin(th2)*r3^2-4*(R2^2*sin(th2)^2*r4^4-2*R2^4*sin(th2)^2*r4^2+6*R2^4*sin(th2)^2*r1^2+6*R2^5*cos(th2)*r1-r3^4*R2^2-4*R2^5*sin(th2)^2*cos(th2)*r1-12*R2^3*sin(th2)^2*r1^3*cos(th2)-2*R2^2*sin(th2)^2*r1^2*r3^2+4*R2^4*sin(th2)^2*cos(th2)^2*r1^2+8*R2^2*cos(th2)^2*r1^2*r4^2+8*R2^2*cos(th2)^2*r1^2*r3^2+4*R2^3*sin(th2)^2*r4^2*cos(th2)*r1-2*R2^4*sin(th2)^2*r3^2+5*R2^2*sin(th2)^2*r1^4+R2^2*sin(th2)^2*r3^4+20*R2^3*cos(th2)*r1^3-8*R2^2*cos(th2)^2*r1^4-8*R2^4*cos(th2)^2*r1^2+4*R2^3*sin(th2)^2*cos(th2)*r1*r3^2-4*R2*cos(th2)*r1*r3^2*r4^2+2*R2*cos(th2)*r1*r4^4-8*R2*cos(th2)*r1^3*r4^2-8*R2^3*cos(th2)*r1*r4^2-8*R2*cos(th2)*r1^3*r3^2+2*R2*cos(th2)*r1*r3^4-8*R2^3*cos(th2)*r1*r3^2-r3^4*r1^2+2*r3^2*r1^4+2*r3^2*R2^4-7*r1^2*R2^4+6*R2*cos(th2)*r1^5+R2^6*sin(th2)^2+2*r1^2*r3^2*r4^2+4*r3^2*r1^2*R2^2-R2^6-r1^6-2*R2^2*sin(th2)^2*r4^2*r3^2-7*r1^4*R2^2-2*R2^2*sin(th2)^2*r4^2*r1^2-r1^2*r4^4+2*r1^4*r4^2-r4^4*R2^2+2*r4^2*R2^4+4*r1^2*r4^2*R2^2+2*r4^2*R2^2*r3^2)^(1/2))-r1^2-r4^2+r3^2)/(-r1+R2*cos(th2))/r4)