Cos2x + sin2x +3sin2x =2

\[\begin{array}{l} \cos 2x + \sin 2x + 3\sin 2x = 2\\ \Leftrightarrow \cos 2x + 4\sin 2x = 2\\ \Leftrightarrow \frac{1}{{17}}\cos x + \frac{4}{{17}}\sin 2x = \frac{2}{{17}}\\ \Leftrightarrow \cos \left( {x - \alpha } \right) = \frac{2}{{17}}\,\,\,\,\,\left( {\cos \alpha = \frac{1}{{17}};\,\,\,\sin \alpha = \frac{4}{{17}}} \right)\\ \Leftrightarrow \left[ \begin{array}{l} x - \alpha = \arccos \frac{2}{{17}} + k2\pi \\ x - \alpha = - \arccos \frac{2}{{17}}k2\pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = \alpha + \arccos \frac{2}{{17}} + k2\pi \\ x = \alpha - \arccos \frac{2}{{17}} + k2\pi \end{array} \right.\,\,\,\left( {k \in Z} \right). \end{array}\]