How to prove that $ \\sin \\angle{GAB}+\\sin \\angle{GBC}+\\sin \\angle{GCA} \\le \\frac{3}{2} $ for a triangle $ABC$ with centroid $G$?

Question

Let $ G $ be the centroid of $ \ riangle ABC $ , such that $ \\measuredangle{GAB}=x,\\measuredangle{GBC}=y,\\measuredangle{GCA}=z $. How do I prove that : $$ \\sin x +\\sin y +\\sin z\\le \\frac{3}{2} $$

Answer 1

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