Cosines and polynomials?

Algebra Level 5

If cos(7207)\cos \left( \frac {720^\circ}{7} \right) is a root of the sixth-degree polynomial

ax6bx4+cx2x1ax^{6}-bx^{4}+cx^{2}-x-1

where a,b,ca, b, c are positive integers, find a+b+ca+b+c.


Bonus: Can you find the monic third degree polynomial with rational coefficients that has cos(7207)\cos (\frac {720^\circ}{7}) as a root?

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