AMC 12A 2021 Spring Problem 22

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

Answer Choices
A. -\dfrac{3}{49}
B. -\dfrac{1}{28}
C. \dfrac{3 \sqrt{7}}{64}
D. \dfrac{1}{32}
E. \dfrac{1}{28}