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I don't want to go through the problem, but some identities that may come in handy are:

1) sin^2(x) + cox^2(x) = 1

-> Rearrange for sin^2(x) and sub into your equation. You then have a quadratic equation in cos(x) - solve it by factoring or using the quadratic formula. (ie let y = cos(x), then you have ay^2 + by + c = 0)

2) sin(2x) = 2sin(x)cos(x) is all you need. Sub that in, and a bit of algebra & factoring will give you the answer.

EDIT: you beat me to it. Good job!

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