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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