Answer
$$\frac{{\sqrt 3 }}{3}$$
Work Step by Step
$$\eqalign{
& \cot \frac{\pi }{3} \cr
& {\text{convert }}\frac{\pi }{3}{\text{radians to degrees}} \cr
& \frac{\pi }{3}{\text{radians}} = \frac{\pi }{3}\left( {\frac{{{{180}^ \circ }}}{\pi }} \right) \cr
& \frac{\pi }{3}{\text{radians}} = {60^ \circ } \cr
& \cot \frac{\pi }{3} = \cot {60^ \circ } \cr
& {\text{using the }}{30^ \circ }{\text{ - 6}}{{\text{0}}^ \circ }{\text{ - 9}}{{\text{0}}^ \circ }{\text{ triangle to obtain}} \cr
& \cot {60^ \circ } = \frac{{{\text{adjacent side to the 3}}{{\text{0}}^ \circ }}}{{{\text{opposite side to the 3}}{{\text{0}}^ \circ }}} \cr
& \cot {60^ \circ } = \frac{1}{{\sqrt 3 }} \cr
& {\text{then }} \cr
& \cot \frac{\pi }{3} = \frac{1}{{\sqrt 3 }} \cr
& or \cr
& \cot \frac{\pi }{3} = \frac{{\sqrt 3 }}{3} \cr} $$
