# Sum of arctangents equals to pi/4

Geometry Level 5

$\arctan\left(\frac{1}{a}\right)+\arctan\left(\frac{1}{b}\right)+\arctan\left(\frac{1}{c}\right)=\frac{\pi}{4}$

Let $$a,b,c$$ be positive integers where $$1 < a \le b\le c$$ such that the equation above is fulfilled. If we denote $$P = a\times b\times c$$, find the sum of all possible values of $$P$$.

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