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 $t = \arctan(2).$  then we have the following $$\tan(t) = 2, y=\sin t = 2/\sqrt 5, x=\cos t = 1/\sqrt 5, 0 < t < \pi/2. $$  to evaluate $$\cot(2t) = \frac{\cos (2t)}{\sin 2t} = \frac{x^2 - y^2}{2xy} = \frac{1-4}{2 \times 1 \times 2} = -\frac34. $$
