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Magic square of fractions featuring the numbers 1-512 each once where the sum of atan² is 2π for each row, column and diagonal

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I think it's Arctan() of the value in the square, and not Arctan()^2 of the value.

I'm not sure how the result was achieved. I know there's an ArcTan addition formula, ArcTan(x) + ArcTan(y) = ArcTan( (x + y) / (1 - x*y) ) for xy < 1. And it looks like all the fractions are less than one. But beyond that it's a mystery.

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