Well it's been a while since I exercised my trig brain so I'm in need of a bit of help with this one. The problem I'm trying to solve is related to this: Problem 202 - Project Euler and part of it involves solving an equation that might look something like this:

I actually know what the solution is to this one (by numerical solving) by I don't know how to achieve it algebraically. Any hints anyone could give would be great.

Thanks