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 $$\large\color{blue}{a\times b\times c\times d\times e\times f}$$.