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Let \alpha,\beta,\gamma be positive real numbers such that \alpha+\beta+\gamma < \pi, \alpha+\beta > \gamma,\beta+\gamma > \alpha, \gamma + \alpha > \beta. Prove that with the segments of lengths \sin \alpha, \sin \beta, \sin \gamma we can construct a triangle and that its area is not greater than
A=\dfrac 18\left( \sin 2\alpha+\sin 2\beta+ \sin 2\gamma \right).

Proposed by Soviet Union

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