Let $ABCD$ be a convex quadrilateral. what is the maximum value: $$P= \sqrt{2}\sin \frac{A}{2}+ \sqrt{3}\sin \frac{B}{2} + \sqrt{6}\sin \frac{C}{2} + \sqrt{3}\sin \frac{D}{2} $$
maximum value $P= \sqrt{2}\sin \frac{A}{2}+ \sqrt{3}\sin \frac{B}{2} + \sqrt{6}\sin \frac{C}{2} + \sqrt{3}\sin \frac{D}{2} $
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inequality