# Déjà vu!

Geometry Level 5

$a^2 \cot 9^\circ + b^2 \cot 27^\circ + c^2 \cot 63^\circ + d^2 \cot 81^\circ$

Let $$a,b,c$$ and $$d$$ be real numbers satisfying $$a+b+c+d=5$$. If the minimum value of the expression above is equal to $$\dfrac{\sqrt x}y$$, where $$x$$ and $$y$$ are coprime positive integers, find $$x+y$$.

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