Assistance with trigonometric inequality needed please

Hey everyone, I'm doing some inequalities and I'm stuck with some trigonometric ones as I've never really encountered them before, some help with the following problem will be greatly appreciated.

Determine Θ, 0<=Θ<=2π so that (π = pi)

$\displaystyle 2 + 3sin-cos2>=0$

What I tried was to replace cos2Θ with $\displaystyle 1 - 2sin^2$ and factorize till I end up with

$\displaystyle (2sin + 1)(sin +1) >= 0$

From there on I'm not certain. I don't want to sinΘ >= -0.5 etc. because I'm afraid that will probably be wrong, How do I proceed? Thanks so much!