Imaginary Factorial?

Calculus Level 5

\[\large | (2i)!| = Ae^{\pi}\sqrt{\frac{\pi}{e^{B\pi}-C}}\]

If the equation above is true for some positive integers \(A\), \(B\) and \(C\), find \(A+B+C\).

Clarification: \(i=\sqrt{-1}\).

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