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