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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