cosx + sinx - 2sinxcosx = 1/2
cosx + sinx(1 - 2cosx) = 1/2
sinx(1 - 2cosx) + cosx - 1/2 = 0
sinx(1 - 2cosx) - 1/2(1 - 2cosx) = 0
(1-2cosx)(sinx - 1/2) = 0
sinx = 1/2 or cosx = 1/2
If sinx = 1/2, then x = π/6 + 2kπ or 5π/6 + 2kπ k = 0, ±1, ±2, ...
If cosx = 1/2, then x = π/3 + 2kπ or 5π/3 + 2kπ