Math is radical!

Algebra Level 3

Consider the following equation 1+2+2(2+2)=a+b+cde+f 1+\sqrt{2}+\sqrt{2\left(2+\sqrt{2}\right)}=\sqrt{\frac{a+\sqrt{b+\sqrt{c}}}{d-\sqrt{e+\sqrt{f}}}} where a,b,c,d,e,f\large\color{#3D99F6}{a,b,c,d,e,f} are integers. Calculate a×b×c×d×e×f\large\color{#3D99F6}{a\times b\times c\times d\times e\times f}.

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