Let y=y(x) be the solution of the differential equation (d y)/(d x)+(√ 2 y)/(2 cos^4 x- cos 2 x)=x e^tan^-1(√ 2 cot 2 x), 0<x<π / 2 with…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{\sqrt{2} y}{2 \cos ^4 x-\cos 2 x}=x \mathrm{e}^{\tan ^{-1}(\sqrt{2} \cot 2 x)}, 0<x<\pi / 2 \text { with } y\left(\frac{\pi}{4}\right)=\frac{\pi^2}{32} . $$ If $\displaystyle y\left(\frac{\pi}{3}\right)=\frac{\pi^2}{18} \mathrm{e}^{-\tan ^{-1}(\alpha)}$, then the value of $\displaystyle 3 \alpha^2$ is equal to \_\_\_\_.