Can't see what Ramanujan did there

Number Theory Level 5

If the infinite continued fraction $\cfrac{1}{1+\cfrac{e^{-2\pi}}{1+\cfrac{e^{-4\pi}}{1+\cdots}}}$ can be expressed as $e^{\dfrac{a\pi}{b}}\left(\sqrt{\dfrac{b+\sqrt{b}}{a}}-\dfrac{c+\sqrt{b}}{a}\right)$ where $a,b$ and $c$ are coprime integers,find $a+b+c$ .