Let $$y = y(x)$$ be the solution curve of the differential equation $$\sin(2x^2) \log_e(\tan x^2) \, dy + \left(4xy - 4\sqrt{2}x \sin\left(x^2 - \frac{\pi}{4}\right)\right) dx = 0$$, $$0 < x < \sqrt{\frac{\pi}{2}}$$, 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