If y=y(x), x ∈(0, π / 2) be the solution curve of the differential equation ( sin^2 2 x) (d y)/(d x)+(8 sin^2 2 x+2 sin 4 x) y=2 e^-4 x(2 sin 2 x+…

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