Is there a way to solve a system of symbolic equations that involve trigonometric equations?

I have the following two matricies:

T = [ cos(theta1 + theta2 + theta3), -sin(theta1 + theta2 + theta3), 0, L2*cos(theta1 + theta2) + L1*cos(theta1) + L3*cos(theta1 + theta2 + theta3);...

sin(theta1 + theta2 + theta3), cos(theta1 + theta2 + theta3), 0, L2*sin(theta1 + theta2) + L1*sin(theta1) + L3*sin(theta1 + theta2 + theta3);...

0, 0, 1, 0;... 0, 0, 0, 1];

S = [cos(phi), -sin(phi), 0 x; sin(phi) cos(phi) 0 y; 0 0 1 0; 0 0 0 1];

phi, x, y, theta1, theta2, theta3, L1, L2, and L3 have all been defined as symbolic variables. I want to set these two 4x4 matrices equal to each other and solve for theta1, theta2 and theta3 in terms of all of the other symbols. Is there a way to do this in MATLAB or am I going to have to pull out the pencil and paper?

[Dan]

I know that there will be multiple solutions, so when I say 'solve' I mean output all of the solutions.