The general value of x satisfying tan x tan 2x = 1 is

tan x tan 2x = 1 

i.e 1 − tan x tan 2x = 0              ...(1) 

Since $\tan 3 x=\tan (x+2 x)$

$=\frac{\tan x+\tan 2 x}{1-\tan x \tan 2 x}$

i.e $\tan 3 x=\infty$   .......(from 1)

i.e $3 x=n \pi+\frac{\pi}{2}$

i. e $x=\frac{n \pi}{3}+\frac{\pi}{6}$