Complex sign. I mean sine!

Algebra Level 4

\[\large \frac{\pi}{A} - i \ln {\left(B+\sqrt{C}\right)} \]

There is no real value for \(\sin^{-1}(2) \) but it has a complex one. And it is of the form as described above where, \(A\), \(B\) and \(C\) are positive integers. Evaluate \(A+B+C\).

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