giải giúp mình với tìm GTLN GTNN của hàm số y=sin2x+√2-sin^2.2x

\[\begin{array}{l} y = \sin 2x + \sqrt 2 - {\sin ^2}2x\\ = - \left( {{{\sin }^2}2x - \sin 2x} \right) + \sqrt 2 \\ = - \left( {{{\sin }^2}2x - 2.\frac{1}{2}\sin 2x + \frac{1}{4}} \right) + \frac{1}{4} + \sqrt 2 \\ = - {\left( {\sin 2x - \frac{1}{2}} \right)^2} + \frac{{4\sqrt 2 + 1}}{4} \le \frac{{4\sqrt 2 + 1}}{4}\\ \Rightarrow Dau\,\, = \,\,\,xay\,\,ra\, \Leftrightarrow \sin 2x = \frac{1}{2}\\ \Leftrightarrow \left[ \begin{array}{l} 2x = \frac{\pi }{6} + k2\pi \\ 2x = \frac{{5\pi }}{6} + k2\pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{{12}} + \frac{{k\pi }}{4}\\ x = \frac{{5\pi }}{{12}} + \frac{{k\pi }}{4} \end{array} \right.\,\,\,\left( {k \in Z} \right).\\ Vay\,\,\,Maxy = \frac{{4\sqrt 2 + 1}}{4}. \end{array}\]