The general solution of the equation $tan x - tan 2 x - tan x tan 2 x = 1$ is

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Solution

Given, $tan x - tan 2 x - tan x tan 2 x = 1$
$\Rightarrow \frac{tan 2 x - tan x}{1 + tan x tan 2 x} = - 1$
$\Rightarrow tan (2 x - x) = tan (- \frac{π}{4})$
$\Rightarrow x = n π - \frac{π}{4}, n \in I$
But $tan 2 (n π - \frac{π}{4}) \to - \infty$
which is not defined( Not in the domain).

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