I have a system of 9 coupled trigonometric equations (a 3X3 Matrix). I am trying to find four unknown angles $\theta_1, \theta_2, \phi_1, \phi_2$ by solving any 4 out of 9 such equations. 
$\text{M}=\left(
\begin{array}{ccc}
 \text{s1xs2x} \cos (\text{$\theta $1}) \cos (\text{$\theta $2}) \cos (\text{$\phi $1}) \cos (\text{$\phi $2})+\text{s1ys2y} \cos (\text{$\theta $1}) \cos (\text{$\theta $2}) \sin (\text{$\phi $1}) \sin (\text{$\phi $2})+\text{s1zs2z} \sin (\text{$\theta $1}) \sin (\text{$\theta $2}) & \text{s1ys2y} \cos (\text{$\theta $1}) \sin (\text{$\phi $1}) \cos (\text{$\phi $2})-\text{s1xs2x} \cos (\text{$\theta $1}) \cos (\text{$\phi $1}) \sin (\text{$\phi $2}) & \text{s1xs2x} \cos (\text{$\theta $1}) \sin (\text{$\theta $2}) \cos (\text{$\phi $1}) \cos (\text{$\phi $2})+\text{s1ys2y} \cos (\text{$\theta $1}) \sin (\text{$\theta $2}) \sin (\text{$\phi $1}) \sin (\text{$\phi $2})-\text{s1zs2z} \sin (\text{$\theta $1}) \cos (\text{$\theta $2}) \\
 \text{s1ys2y} \cos (\text{$\theta $2}) \cos (\text{$\phi $1}) \sin (\text{$\phi $2})-\text{s1xs2x} \cos (\text{$\theta $2}) \sin (\text{$\phi $1}) \cos (\text{$\phi $2}) & \text{s1xs2x} \sin (\text{$\phi $1}) \sin (\text{$\phi $2})+\text{s1ys2y} \cos (\text{$\phi $1}) \cos (\text{$\phi $2}) & \text{s1ys2y} \sin (\text{$\theta $2}) \cos (\text{$\phi $1}) \sin (\text{$\phi $2})-\text{s1xs2x} \sin (\text{$\theta $2}) \sin (\text{$\phi $1}) \cos (\text{$\phi $2}) \\
 \text{s1xs2x} \sin (\text{$\theta $1}) \cos (\text{$\theta $2}) \cos (\text{$\phi $1}) \cos (\text{$\phi $2})+\text{s1ys2y} \sin (\text{$\theta $1}) \cos (\text{$\theta $2}) \sin (\text{$\phi $1}) \sin (\text{$\phi $2})-\text{s1zs2z} \cos (\text{$\theta $1}) \sin (\text{$\theta $2}) & \text{s1ys2y} \sin (\text{$\theta $1}) \sin (\text{$\phi $1}) \cos (\text{$\phi $2})-\text{s1xs2x} \sin (\text{$\theta $1}) \cos (\text{$\phi $1}) \sin (\text{$\phi $2}) & \text{s1xs2x} \sin (\text{$\theta $1}) \sin (\text{$\theta $2}) \cos (\text{$\phi $1}) \cos (\text{$\phi $2})+\text{s1ys2y} \sin (\text{$\theta $1}) \sin (\text{$\theta $2}) \sin (\text{$\phi $1}) \sin (\text{$\phi $2})+\text{s1zs2z} \cos (\text{$\theta $1}) \cos (\text{$\theta $2}) \\
\end{array}
\right)$

I have the numerical value of the matrix elements $M=\left(
\begin{array}{ccc}
 144.57 & -2.21141 & 149.231 \\
 -10.5118 & 8.78583 & 10.3137 \\
 28.3015 & 14.5596 & 16.4425 \\
\end{array}
\right)$

Also, s1xs2x = 17.1482, s1ys2y = -17.1482, s1zs2z = 210.153

My code looks like this: 
```Mathematica
Sol = N@Reduce[{s1xs2x*Cos[Theta1]*Cos[Theta2]*Cos[Phi1]*Cos[Phi2] + s1zs2z*Sin[Theta1]*Sin[Theta2] + s1ys2y*Cos[Theta1]*Cos[Theta2]*Sin[Phi1]*Sin[Phi2] == M[[1,1]], 
    s1ys2y*Cos[Theta1]*Cos[Phi2]*Sin[Phi1] - s1xs2x*Cos[Theta1]*Cos[Phi1]*Sin[Phi2] == M[[1,2]], 
    (-s1zs2z)*Cos[Theta2]*Sin[Theta1] + s1xs2x*Cos[Theta1]*Cos[Phi1]*Cos[Phi2]*Sin[Theta2] + s1ys2y*Cos[Theta1]*Sin[Theta2]*Sin[Phi1]*Sin[Phi2] == M[[1,3]], 
    s1ys2y*Cos[Phi1]*Cos[Phi2] + s1xs2x*Sin[Phi1]*Sin[Phi2] == M[[2,2]], 0 < Theta1 < Pi, 0 <Theta2 < Pi, 0 < Phi2 < Pi, 0 < Phi2 < Pi},{Theta1, Theta2, Phi1, Phi2}]
```

However, it keeps on running forever. I am not sure where I'm going wrong. Any help shall be highly appreciated.