IMO 1985 LL GDR37

Prove that a triangle with angles \alpha, \beta, \gamma, circumradius R, and

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IMO 1985 LL GDR37

Origin: GDR

Problem

Prove that a triangle with angles \alpha, \beta, \gamma, circumradius R, and area A satisfies tan \alpha 2 + tan \beta 2 + tan \gamma 2 \leq9R2 4A .