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If the infinite continued fraction 11+e−2π1+e−4π1+⋯ \cfrac{1}{1+\cfrac{e^{-2\pi}}{1+\cfrac{e^{-4\pi}}{1+\cdots}}}1+1+1+⋯e−4πe−2π1 can be expressed as eaπb(b+ba−c+ba)e^{\dfrac{a\pi}{b}}\left(\sqrt{\dfrac{b+\sqrt{b}}{a}}-\dfrac{c+\sqrt{b}}{a}\right)ebaπ⎝⎛ab+b−ac+b⎠⎞ where a,ba,ba,b and ccc are coprime integers,find a+b+ca+b+ca+b+c.
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