General advice on unsolvable equations

http://img232.imageshack.us/img232/9...mulaud2.th.jpg

t and horax are angles.

r, MC and VM are distances.

I'd like to solve for t, but math softwares tell me they find no solution.

While I'd very much appreciate a solution to the specific problem at hand, I am also very interested in how one should proceed on occasions like this. What I know to do is to make guesses and close in on a solution with the bisection method (or Newton Raphson if tehre is a derivative). But are there other approaches?

**Could one use some statistics approach where one samples a lot of guesses on different parameter values and then fit new and simple functions t = f(horax,r,MC,VM) to that data?**

I'd appreciate any advice!