Simplifying binomial sums

Simplifying binomial sums

What would be the easiest way to see (or show) that \begin{equation*}
\sum_{k=0}^n \binom{n}{k} \left( (i \sqrt{3})^k-(-i \sqrt{3})^k\right) = i
2^{n+1} \sin \left({\frac{\pi n}{3}} \right) \end{equation*} and
\begin{equation*} \sum_{k=0}^n \binom{n}{k} (-1)^{n-k} \left( (i
\sqrt{3})^k-(-i \sqrt{3})^k\right) = i 2^{n+1} \sin \left({\frac{\pi
n}{3}} \right) ? \end{equation*}