Cosines and polynomials?

Algebra Level 5

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

\[ax^{6}-bx^{4}+cx^{2}-x-1\]

where \(a, b, c\) are positive integers, find \(a+b+c\).


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

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