Cos^2x+3sin^2x+2√3sinxcosx=3 Решите плиз

Решите задачу:

$cos^2x + 3sin^2x + 2 \sqrt{3} sinxcosx = 3 \\ \\ cos^2x + 3sin^2x -3 + 2 \sqrt{3} sinxcosx = 0 \\ \\ cos^2x - 3cos^2x + 2 \sqrt{3} sinxcosx = 0 \\ \\ -2cos^2x + 2\sqrt{3} cosxsinx = 0 \\ \\ 2cos^2x - 2 \sqrt{3}cosxsinx = 0 \\ \\ cosx(2cosx - 2 \sqrt{3}sinx) = 0 \\ \\cosx = 0 \\ \\ \boxed{x = \dfrac{ \pi }{2} + \pi n, \ n \in Z} \\ \\ cosx - \sqrt{3}sinx = 0 \\ \\ cosx = \sqrt{3} sinx \\ \\ ctgx = \sqrt{3} \\ \\ \boxed{x = \dfrac{ \pi }{6} + \pi n, \ n \in Z.}$