I'm not sure what I'm missing here:
Solve for θ in terms of a and b.
Every attempt I've made has gotten rather messy.
--Kevin C.
I think a lot of times as math students we want a nice or "pretty" if you will solution to problems. Sometimes though, we get solutions that look messy and automatically think they must be wrong.
I do this all the time.
Eventually, you will learn to trust and not doubt yourself so much!