Find the general solution of $tan x + tan 2 x + tan x tan 2 x = 1$

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Solution

$tan x + tan 2 x + tan x tan 2 x = 1$
$tan x + tan 2 x = 1 - tan x tan 2 x$
$\frac{tan x + tan 2 x}{1 - tan x tan 2 x} = 1$
$tan (x + 2 x) = 1$
$tan 3 x = 1$
$3 x = \frac{π}{4}$
$3 x = n π + \frac{π}{4}$
$x = \frac{n π}{3} + \frac{π}{12}$
$x = \frac{π}{12} (4 n + 1)$

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