HMMT 2001 T8

Express $\frac{\sin 10+\sin 20+\sin 30+\sin 40+\sin 50+\sin 60+\sin 70+\sin 80}{\cos 5 \cos 10 \cos 20}$ without using trigonometric functions.

Dataset text NuminaMath olympiads. Quoted with source.

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4 \sqrt{2}

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