Double square

Algebra Level 3

{a=45ab=4+5bc=45+cd=4+5+d\begin{cases} a=\sqrt{4-\sqrt{5-a}} \\ b=\sqrt{4+\sqrt{5-b}} \\ c=\sqrt{4-\sqrt{5+c}} \\ d=\sqrt{4+\sqrt{5+d}} \end{cases}

Find the product abcd.abcd.


Hint: You don't need to find any of the individual variables!

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