A trigonometric inequality

Algebra Level 5

Find the smallest integer \(N\) such that for all positive integers \(n\) \[ \lvert \sin \frac{1}{100}+\sin \frac{2}{100}+...+\sin \frac{n}{100} \rvert <N\]

Details and assumptions

You may use the fact that \(\pi \) is an irrational number.

Clarification: The measurements are done in radians, not degrees.

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