# I'm back problem (Double Euler's?)

Algebra Level 4

$\large \ln(k) = \exp\left[ -\ln(3) + i \sin^{-1} \left( \frac{24}{25} \right) \right]$

Suppose we define $$k$$ such that the equation above is fulfilled, and if the imaginary part of $$k$$ can be expressed in the form of $\large e^{\frac AB} \sin\left( \frac CD\right)$

where $$A,B,C$$ and $$D$$ are positive integers such that $$\gcd(A,B) = \gcd(C,D) = 1$$, find the value of $$A+B+C+D$$.

Details and Assumptions

We define $$\exp (x)$$ as $$e^x$$.

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