Trigonometrical Inequality?

For $x, y \in \mathbb R$ with $0 < x < \frac { \pi }{ 2 }$ such that

$\large \frac {(\sin x)^{2y}}{(\cos x)^{\frac {y^2}2}} +\frac {(\cos x)^{2y}}{(\sin x)^{\frac {y^2}2}} = \sin 2x$

then find the value of $y$ .