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

Algebra Level 4

ln(k)=exp[ln(3)+isin1(2425)]\large \ln(k) = \exp\left[ -\ln(3) + i \sin^{-1} \left( \frac{24}{25} \right) \right]

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

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

Details and Assumptions

We define exp(x)\exp (x) as exe^x.


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