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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