Clearly we need to get trig functions of a single angle, so let's use the double angle identity for sin(2x):
Our equation has a mixture of sinx and cosx to various powers; but it also has that "+1" that makes it impossible to work with the equation in this form.
But here is a place where you use the basic trig identity in an unusual way to make the problem easy to solve.
We need a reference angle of pi/3 in the 2nd and 4th quadrants; the solutions between 0 and 2pi are 2pi/3 and 5pi/3.
