# Tri-angular "Angular" Inequality!

Geometry Level 4

$P = 2\sin \dfrac A2 + \sin B + \sin C$

Let $$A,B$$ and $$C$$ denote the angles of a triangle. Find the maximum value of $$P$$.

Give your answer as $$\lfloor 10^4 \times P \rfloor$$.

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