What is the general formula for the degree of the minimal polynomial of $\sin(\pi/m)$? There are plenty of questions on this site asking for particular $m$, and I know that this has some connection to the Chebyshev polynomials, but I can't seem to find any good source with a straight answer.
If this question doesn't have any known simple answers, then are there any inequalities, perhaps of the type $\deg(m)\geq \varphi(m)/2$?