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ILL 1985 Problem 12

    Find the maximum value of sin⁡2θ1+sin⁡2θ2+⋯+sin⁡2θn\sin^2 \theta_1+\sin^2 \theta_2+\cdots+\sin^2 \theta_n subject to the restrictions 0≤θi,θ1+θ2+⋯+θn=π.0 \leq \theta_i , \theta_1+\theta_2+\cdots+\theta_n=\pi.

    Dataset text AI-MO AoPS. Quoted with source.

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