Answer
$-\frac{\sqrt 3}{3}$
Work Step by Step
As $330^{\circ}$ and $(330^{\circ}-360^{\circ})=-30^{\circ}$ are coterminal, we can write:
$\tan 330^{\circ}=\tan(-30^{\circ})$
$\tan (-x)=-\tan x$
$\tan (-30^{\circ})=-\tan 30^{\circ}=-\frac{\sqrt 3}{3}$