Find the $p a r t i c u l a r s o l u t i o n$ of $tan x + tan 2 x + tan x . tan 2 x = 1$ .

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Solution

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

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