# Tanx + tan2x +tan3x = tanxtan2xtan3x

$\begin{array}{l} \tan x+\tan 2 x+\tan 3 x=\tan x \cdot \tan 2 x \cdot \tan 3 x \\ \tan x+\tan 2 x=\tan x \cdot \tan 2 x \cdot \tan 3 x-\tan 3 x \\ \tan x+\tan 2 x=\tan 3 x(\tan x \cdot \tan 2 x-1) \\ \tan x+\tan 2 x \\ \tan 3 x \tan x-1 \\ \tan x(x+2 x)=-\tan 3 x \\ \tan (x+2 x)=-\tan 3 x \\ \tan 3 x=-\tan 3 x \\ \tan 3 x=0 \\ \tan 3 x=0 \\ 3 x=0, \pi, 2 \pi, 3 \pi \\ x=0, \frac{\pi}{3}, \frac{2}{3} \pi, \pi \end{array}$

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