Imaginary Trigonometry

Geometry Level 4

\[x= \frac{\pi}{2}- i \ln \left ( \frac{a \pm \sqrt{b}}{c} \right ) \]

The principal solution to the equation \( \sin x =\frac{3}{2} \) can be written in the form above.

What is the value of \(a+b+c\)?

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

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