Answer
4 + 2$\sqrt 3$
or 2 (2 + $\sqrt 3$)
Work Step by Step
Given expression
= $( \tan 45^{\circ} + \tan 60^{\circ})^{2}$
= $ ( 1+ \sqrt 3)^{2}$
( substituting for exact values of trigonometric functions)
= ( 1 + $2\sqrt 3 $ + 3)
[ on expanding using identity $(a+b)^{2} = a^{2} + 2ab + b^{2}$]
= 4 + 2$\sqrt 3$
or 2 (2 + $\sqrt 3$)
