Let $y=y(x)$ be the solution curve of the differential equation $\sin \left(2 x^{2}\right) \log _{e}

Question

Let $y=y(x)$ be the solution curve of the differential equation $\sin \left(2 x^{2}ight) \log _{e}\left(	an x^{2}ight) d y+\left(4 x y-4 \sqrt{2} x \sin \left(x^{2}-\frac{\pi}{4}ight)ight) d x=0$, $0<x<\sqrt{\frac{\pi}{2}}$, which passes through the point $\left(\sqrt{\frac{\pi}{6}}, 1ight)$. Then $\left|y\left(\sqrt{\frac{\pi}{3}}ight)ight|$ is equal to

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