# Extrema(s) of Trigonometric Functions!

Geometry Level 5

$\large{\left( \sin(A) + \sin(B) + \sin(C) \right) \left( \dfrac1A + \dfrac1B + \dfrac1C \right)}$

Let $$A,B,C$$ be the angles (in radians) of a triangle. If the minimum value of the above expression can be expressed as:

$\large{\dfrac{\sqrt{A^B}}{C \cdot \pi^D}}$

such that $$A, B, C,D$$ are positive integers, find the minimum value of $$A+B+C+D$$?

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