If $\tan (x + y) = 33$ and $x = \tan^{-1}(3)$,then $y$ will be

The solution of $\tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}$ is

$\tan^{-1} \left( \frac{\sqrt{1 + x^2} - 1}{x} \right) = $

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

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3}$ for $-1 < x < 1$ and $x \neq 0$ is $\alpha-\frac{4}{\sqrt{3}}$,then $\alpha$ is equal to $..........$.

$4 \tan^{-1} \frac{1}{5} - \tan^{-1} \frac{1}{239}$ is equal to