sin 80 is a root

Let $x = \sin 80^{\circ}$ be one of the zeros of the polynomial $$P(x) = a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0$$ such that $a_6 > 0$ and the $a_i$’s are coprime integers. Determine the value of $|a_0| + |a_2| + |a_4| + |a_6|$.