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Omni-MATH / Express (sin10+sin20+sin30+sin40+sin50+sin60+sin70+sin80)/(cos5cos10cos20) without using trigonometric functions.

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problem

Express sin10+sin20+sin30+sin40+sin50+sin60+sin70+sin80cos5cos10cos20\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.
Plain-text mathematical notation (without MathML)
Express (sin10+sin20+sin30+sin40+sin50+sin60+sin70+sin80)/(cos5cos10cos20) without using trigonometric functions.
Original LaTeX notation
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.

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