Answer
$2+\sqrt 3$
Work Step by Step
$tan75^\circ=tan(45+30)^\circ
=\frac{tan45^\circ+tan30^\circ}{1-tan45^\circ tan30^\circ}
=\frac{1+\sqrt 3/3}{1-\sqrt 3/3}
=\frac{3+\sqrt 3}{3-\sqrt 3}
=\frac{3+\sqrt 3}{3-\sqrt 3}\times\frac{3+\sqrt 3}{3+\sqrt 3}
=\frac{12+6\sqrt 3}{6}
=2+\sqrt 3$
