Prove that if $\displaystyle n > 2$, then $\displaystyle \mathbb{U}_n$ has a subgroup of order $\displaystyle 2$.

There must exist a $\displaystyle g \in \mathbb{U}_n$ such that $\displaystyle g^2 \equiv 1 \pmod{n}$. How do I know there exists such an element in $\displaystyle \mathbb{U}_n$?