# Rational values for $\sin\left(\frac{2\pi }{n}\right)$

I want to find for what $n\in \mathbb{N}$ a $n$-sided polygon has rational area, assuming the polygons' "long" radius is $1$. This reduces to whether or not $\sin\left(\frac{2\pi }{n}\right)$ is rational.

Solutions for $n$ found so far include $1, 2, 4, 12$. Have not found a corresponding sequence on OEIS.

Thanks.