\( \text { If } I=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x d x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \…

\(
\text { If } I=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x d x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \text {, then the value of definite integration } \int_0^{2 I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} d x \text { is }
\)