The value of $\int\limits_{0}^{\pi/2}\large\frac{\cos^{5/3}x}{\cos^{5/3}x+\sin^{5/3}x}$$dx$ is

Question

$$\begin{array}{1 1}(1)\frac{\pi}{2}&(2)\frac{\pi}{4}\\(3)0&(4)\pi\end{array}$$