the problem im having trouble with is: solve 1 + cos(2x) = 2sin^2(2x) for x, where 0 ≤ x < 2π

i set everything equal to 0 and worked it down to (cos(2x) + 1)(2cos(2x) - 1) = 0 and solved each of those individually getting x = π/2 and x = π/6 but I'm not even sure if everything is correct to that point or how to finish the problem off from there if I was going on the right direction. any help would be much appreciated. thanks