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$\tan 3 x \tan 2 x \tan x=\tan 3 x-\tan 2 x-\tan x$

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We know that $3 x=2 x+x$

Therefore, $\tan 3 x=\tan (2 x+x)$

or $\tan 3 x=\frac{\tan 2 x+\tan x}{1-\tan 2 x \tan x}$

or $\tan 3 x-\tan 3 x \tan 2 x \tan x=\tan 2 x+\tan x$

or $\tan 3 x-\tan 2 x-\tan x=\tan 3 x \tan 2 x \tan x$

or $\tan 3 x \tan 2 x \tan x=\tan 3 x-\tan 2 x-\tan x$

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