Let $f: R \rightarrow R$ be given $f(x)=\tan x$. Then, $f^{-1}(1)$ is

If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then $x(y+z)+y(z+x)+z(x+y)$ equals to

If $2 \sin ^{-1} x-3 \cos ^{-1} x=4, x \in[-1,1]$, then $2 \sin ^{-1} x+3 \cos ^{-1} x$ is equal to

If $$\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\cos ^{-1}\left(\frac{1-a^2}{1+a^2}\right)=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$ where $$a, x \in(0,1)$$, then the value of $$x$$ is