Answer
$ 2-\sqrt 3$
Work Step by Step
$tan15^\circ=tan(45^\circ-30^\circ)=\frac{tan45^\circ-tan30^\circ}{1+tan45^\circ tan30^\circ}=\frac{1-\frac{\sqrt 3}{3}}{1+\frac{\sqrt 3}{3}}=\frac{3-\sqrt 3}{3+\sqrt 3}=\frac{3-\sqrt 3}{3+\sqrt 3}\times\frac{3-\sqrt 3}{3-\sqrt 3}=\frac{12-6\sqrt 3}{6}=2-\sqrt 3$
