Differential Equations: JEE Main 2022 Mathematics question

If $y=y(x), x \in(0, \pi / 2)$ be the solution curve of the differential equation $\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=2 \mathrm{e}^{-4 x}(2 \sin 2 x+\cos 2 x)$, with $y(\pi / 4)=\mathrm{e}^{-\pi}$, then $y(\pi / 6)$ is equal to :