With today's graphing calculators the easiest way to solve this equation is to graph it.
There are 6 roots in the interval [0,2π]
They are π/6, π/2, 5π/6,7π/6, 3π/2 and 11π/6..
Right off I don't see an easy way analytically. Usually the best first approach is to convert to all sines and cosines
Just quick and dirty: if you convert to sines and cosines, you will get equation from which you can divide out cos x, which means values where cos x = 0 solve the problem.
Then you will have an equation in sin and sin2 which has as solution sin x = ±1/4.
I didn't pursue this, but you should start there.
