As easy as e^pi

Calculus Level 5

\[ \large \displaystyle \sum_{n=1}^{\infty} \dfrac{1}{n^{2}-2} = \dfrac{A}{B} -\dfrac{i\pi}{C\sqrt{C}}\left[\dfrac{e^{i\pi\sqrt{D}}+e^{-i\pi\sqrt{D}}}{e^{i\pi\sqrt{E}}-e^{-i\pi\sqrt{E}}}\right] \] If the above equation is true for positive and not necessarily distinct integers \(A,B,C,D,E\)
where \(C,D,E\) can't be factorised further, and \(i=\sqrt{-1}\), then
find, \[ \large \phi(A+B+C+D+E)\] where \(\phi(n)\) is the Euler-Totient Function

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