Vexing cosines

Geometry Level 4

\[\cos ^{ 3 }15^\circ+\cos ^{ 3 }25^\circ+\cos ^{ 3 }55^\circ+\cos ^{ 3 }65^\circ+ \cos ^{ 3 }95^\circ+ \\ \cos ^{ 3 }105^\circ+\cos ^{ 3 }135^\circ+\cos ^{ 3 }145^\circ+\cos ^{ 3 }185^\circ\]

Find the value of the sum above correct to three decimals.

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