10.1

Part of 2021 Kyiv City MO Round 1

Problems(1)

Hardest problem on Kyiv City MO 2021. Possibly ever

Source: Kyiv City MO 2021 Round 1, Problem 10.1

Prove the following inequality:

\sin{1} + \sin{3} + \ldots + \sin{2021} > \frac{2\sin{1011}^2}{\sqrt{3}}

Proposed by Oleksii Masalitin