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