Halving An Angle Many Times

Geometry Level 3

(sin152sin27.5)(sin15+2cos27.5)=?\large (\color{#D61F06}{\sin 15^\circ} - \color{#3D99F6}{2\sin^2 7.5^\circ})(\color{#D61F06}{\sin 15^\circ} + \color{#3D99F6}{2\cos^2 7.5^\circ})= \, ?

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