Math is radical!

Algebra Level 3

Consider the following equation \[ 1+\sqrt{2}+\sqrt{2\left(2+\sqrt{2}\right)}=\sqrt{\frac{a+\sqrt{b+\sqrt{c}}}{d-\sqrt{e+\sqrt{f}}}} \] where \(\large\color{blue}{a,b,c,d,e,f}\) are integers. Calculate \(\large\color{blue}{a\times b\times c\times d\times e\times f}\).