Trigonometry Problem

$\begin{aligned} x & = {\color{#3D99F6}\tan 200^\circ} \left(\cot 10^\circ - \tan 10^\circ \right) & \small \color{#3D99F6} \tan (180^\circ - x) = - \tan x \\ & = {-\color{#3D99F6}\tan (-20^\circ)} \left(\frac 1{\tan10^\circ} - \tan 10^\circ \right) & \small \color{#3D99F6} \tan (- x) = - \tan x \\ & = \tan 20^\circ \left(\frac {1-\tan^2 10^\circ}{\tan 10^\circ} \right) \\ & = {\color{#3D99F6}2}\tan 20^\circ \left(\frac {1-\tan^2 10^\circ}{{\color{#3D99F6}2}\tan 10^\circ} \right) & \small \color{#3D99F6} \tan 2x = \frac {2\tan x}{1-\tan^2 x} \\ & = 2\tan 20^\circ \left(\frac 1{\tan 20^\circ} \right) \\ & = \boxed{2} \end{aligned}$