Answer
Exact value of $\tan 750^{\circ}$ = $\frac{1}{\sqrt 3}$ or $\frac{\sqrt 3}{3}$
Work Step by Step
To find exact value of $\tan 750^{\circ}$, let's find its reference angle first.
$ 750^{\circ} = 2\times360^{\circ} + 30^{\circ}$
Thus $ 750^{\circ}$ terminates in quadrant I and its reference angle is $30^{\circ}$
As $ 750^{\circ}$ terminates in quadrant I, its $\tan$ will be positive. Therefore by reference angle theorem-
$\tan 750^{\circ}$ = $\tan 30^{\circ}$
= $\frac{1}{\sqrt 3}$
= $\frac{\sqrt 3}{3}$
