Inverse Inequality!

Geometry Level 4

\[\large P = 2 \arctan \left( \dfrac{A}{2}\right) + \arctan(B) + \arctan (C)\]

Given that \(A, B, C\) are positive reals such that \(A+B+C = 4\).

Submit your answer as \(\lfloor 10000 \max(P) \rfloor\).

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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