1966 IMO Problems/Problem 2

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Let $A$, $B$, and $C$ be the lengths of the sides of a triangle, and \[ a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta respectively, the angles opposite these sides.

\[a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta})\]

Prove that if the triangle is isosceles.