If 4 sin 2 x sin 4 x + sin 2 x = 3 , then x =

Simplify the given expression

$4\left(\sin 2x\sin 4x+{\sin }^{2}x\right)=3$

$\Rightarrow 2(\cos 2x-\cos 6x)+2(1-\cos 2x)=3$

$\Rightarrow 2\cos 2x-2\cos 6x+2-2\cos 2x=3$

$\Rightarrow -2\cos 6x+2=3$

$\Rightarrow \cos 6x=-\frac{1}{2}$

Therefore, $6x=2\pi n\pm \frac{2\pi }{3}$

$\Rightarrow x=\frac{2n\pi }{6}\pm \frac{2}{6}\times \frac{\pi }{3}$

$\Rightarrow x=\frac{n\pi }{3}\pm \frac{\pi }{9}$