I've tried several ways again. This last one I tried multiplying by the complex conjugate but that led me nowhere near the answer I needed unless I messed up (shown below). I'm not gonna type all of the work I did because it's just too tedious doing the latex. I basically got the it down to:
I think what I would do is first change everything to sine and cosine (just because I am more comfortable with them than with the other functions!):
Now, get common denominators for the fractions on the left: .
Add the two fractions and use the fact that and you are home!