One more of those

Geometry Level 4

$\cos(8^\circ)+\cos(16^\circ)+\cos(32^\circ)+\cos(56^\circ)+\ldots+\cos(k^\circ)+\ldots+\cos(352^\circ)$ Find the sum above, where $$0<k<360$$ and $$\gcd(k,360)=8$$.

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