# Sum of arctangents equals to pi/4, part 2

Geometry Level 5

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

Let $$a,b,c, d$$ be positive integers where $$1 < a \le b\le c \le d$$ such that the equation above is fulfilled. What is the largest possible value of $$d$$?

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