# Cotangents

Geometry Level pending

Given that $$x$$ and $$y$$ are positive numbers satisfying

$$x-y= \dfrac\pi4$$ and

$$\cot x + \cot y = 2$$.

And if the minimum value of $$x+y$$ is equal to $$\dfrac ab\pi$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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