I have been having a lot of problems with trig identities and their use in solving formulae, and wondered if anyone could help me out with this.

The following is an equation which I thought I had solved but my answer is different from that provided by my book, so I must have made a mistake. The problem is, I can't see where.

Solve the equation

One of my big difficulties with this kind of question is knowing which identity to use.

For example, in this question, saying means there are three possible starting points:

or

or

[

After looking at these three possibilities, I decided the second may be the best as everything is in terms of cos theta and it's quadratic...

=

And factorizing this:

So or [. The latter is outside the domain, so can be discounted.

But this is not what the books says the answer should be ()

I would really appreciate it if anyone could tell me what's going wrong here because these trig identities are really giving me a hard time..!