The solutions of the equation 1 + sin 2 x sin 2 x sin 2 x cos 2 x 1 + cos 2 x cos 2 x 4 sin 2 x 4 sin 2 x 1…

$\left|\begin{array}{ccc}1+{\sin }^{2}x& {\sin }^{2}x& {\sin }^{2}x\\ {\cos }^{2}x& 1+{\cos }^{2}x& {\cos }^{2}x\\ 4\sin 2x& 4\sin 2x& 1+4\sin 2x\end{array}\right|=0$

use $R_1\to R_1+R_2+R_3$

$\Rightarrow \left(2+4\sin 2x\right)\left|\begin{array}{ccc}1& 1& 1\\ {\cos }^{2}x& 1+{\cos }^{2}x& {\cos }^{2}x\\ 4\sin 2x& 4\sin 2x& 1+4\sin 2x\end{array}\right|=0$

use $C_1\to C_1-C_{3 } \& C_2\to C_2-C_{3 }$

$\Rightarrow \left(2+4\sin 2x\right)\left|\begin{array}{ccc}0& 0& 1\\ 0& 1& {\cos }^{2}x\\ -1& -1& 1+4\sin 2x\end{array}\right|=0$

$\Rightarrow \left(2+4\sin 2x\right)=0$

$\Rightarrow \sin 2x=-\frac{1}{2}$

$\Rightarrow 2\mathrm{x}=\pi +\frac{\pi }{6},2\pi -\frac{\pi }{6}$

$\mathrm{x}=\frac{\pi }{2}+\frac{\pi }{12},\pi -\frac{\pi }{12}$