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If cos(720∘7)\cos \left( \frac {720^\circ}{7} \right)cos(7720∘) is a root of the sixth-degree polynomial
ax6−bx4+cx2−x−1ax^{6}-bx^{4}+cx^{2}-x-1ax6−bx4+cx2−x−1
where a,b,ca, b, ca,b,c are positive integers, find a+b+ca+b+ca+b+c.
Bonus: Can you find the monic third degree polynomial with rational coefficients that has cos(720∘7)\cos (\frac {720^\circ}{7})cos(7720∘) as a root?
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