2021 AMC 12A Problem 22

Suppose that the roots of the polynomial P(x)=x^3+ax^2+bx+c are \cos \frac{2\pi}7,\cos \frac{4\pi}7, and \cos \frac{6\pi}7, where angles are in radians. What is abc?

\textbf{(A) }{-}\frac{3}{49} \qquad \textbf{(B) }{-}\frac{1}{28} \qquad \textbf{(C) }\frac{\sqrt[3]7}{64} \qquad \textbf{(D) }\frac{1}{32}\qquad \textbf{(E) }\frac{1}{28}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.