Differential Equations: JEE Main 2022 Mathematics question

Let $y=y(x)$ be the solution curve of the differential equation $\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x^2}} \right)dy + \left( {4xy - 4\sqrt 2 x\sin \left( {{x^2} - {\pi \over 4}} \right)} \right)dx = 0$, $0 < x < \sqrt {{\pi \over 2}}$, which passes through the point $\left(\sqrt{\frac{\pi}{6}}, 1\right)$. Then $\left|y\left(\sqrt{\frac{\pi}{3}}\right)\right|$ is equal to ______________.