sin 3x + cos 2x = 0

I need to solve for x between the interval [0,2pi)

In the previous chapter there was a problem that wanted us to prove that sin 3x = 3cos^2xsinx-sin^3x so i decided to try using that. However i'm not sure if i'm going down the right path. How would you guys do it?

Wolfram Alpha also got

2(pi * n-tan inverse(1+(root 5)+(root 5 +2(root5))) I'm not sure how to get tan out of all that stuff.

~anonymous