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:
\( \dfrac{2}{\sqrt{3}} e^{-2\pi/3} \)
\( \dfrac{2}{\sqrt{3}} e^{2\pi/3} \)
\( \dfrac{1}{\sqrt{3}} e^{-2\pi/3} \)
\( \dfrac{1}{\sqrt{3}} e^{2\pi/3} \)
