How to evaluate $\cot(2\arctan(2))$? How do you evaluate the above?
I know that $\cot(2\tan^{-1}(2)) = \cot(2\cot^{-1}\left(\frac{1}{2}\right))$, but I'm lost as to how to simplify this further.

Let $y=\cot(2\arctan 2)$. You can use the definition $\cot x\equiv \frac{1}{\tan x} $ and the identity for $\tan 2x\equiv\frac{2\tan x}{1-\tan^2 x}$ to find $\frac 1y=\tan(2 \arctan 2)$ in terms of $\tan(\arctan 2) = 2$.
