#andy
\[\begin{array}{l}
{\cos ^2}x = 3\sin 2x + 3\\
\Rightarrow {\cos ^2}x = 6\sin x\,\cos x + 3\\
\cos x = 0 \Rightarrow VN\\
\cos x \ne 0\\
\Rightarrow 1 = 6\tan x + 3\left( {1 + {{\tan }^2}x} \right)\\
\Leftrightarrow \tan x = \frac{{ - 3 \pm \sqrt 3 }}{3}\\
\Leftrightarrow x = \arctan \left( {\frac{{ - 3 \pm \sqrt 3 }}{3}} \right) + k\pi
\end{array}\]