# 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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