Answer
$$\sqrt 3 $$
Work Step by Step
$$\eqalign{
& \tan \frac{\pi }{3} \cr
& {\text{Use the identity }}\tan \theta = \frac{{\sin \theta }}{{\cos \theta }} \cr
& \tan \frac{\pi }{3} = \frac{{\sin \left( {\pi /3} \right)}}{{\cos \left( {\pi /3} \right)}} \cr
& {\text{From the unit circle we known that }} \cr
& \sin \frac{\pi }{3} = \frac{{\sqrt 3 }}{2}{\text{ and cos}}\frac{\pi }{3} = \frac{1}{2} \cr
& {\text{Then}} \cr
& \tan \frac{\pi }{3} = \frac{{\sqrt 3 /2}}{{1/2}} \cr
& {\text{Simplifying}} \cr
& \tan \frac{\pi }{3} = \sqrt 3 \cr} $$
