The following question appeared in an examination:

Given that $\tan x=\sqrt{3}$, find the possible values of $\sin 2x$.

A student gave the following answer:

$\tan x=\sqrt{3}$ so $x=60^{\circ }$ and $2x=120^{\circ }$, therefore $\sin 2x=\frac{\sqrt{3}}{2}$.

Which one of the following statements is correct?