If $\sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5}$, then $\cos ^{-1} x+\sin ^{-1} y$ is

The value of the expression $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ is

The range of $\sec ^{-1} x$ is

If $\tan ^{-1} x+\tan ^{-1} y=\frac{4 \pi}{5}$, then $\cot ^{-1} x+\cot ^{-1} y$ is equal to