In my field theory lecture notes I have it that a regular polygon with $n$ sides is constructable iff $\zeta_{n}=\frac{2\pi}{n}$ is constructable.
Shouldn't this be $\frac{\pi}{n}$ instead of $\frac{2\pi}{n}$ ? (since each angle of a regular polygon with $n$ sides is $\frac{\pi}{n}$ and not $\frac{2\pi}{n}$)