ArcTan[(2 Sqrt[z^2 - 1])/(-2 + z^2)] == (Pi/(2 Sqrt[-1 + z^2])) (2 Sqrt[1 - 1/z^2] z + (-2 + z^2) Sqrt[z^4/(-1 + z^2)] Sqrt[(-1 + z^2)/z^4] Sqrt[(-1 + z^2)/(-2 + z^2)^2] - Sqrt[1 - 1/z^2] z (Sqrt[I/z] Sqrt[(-I) z] - Sqrt[-(I/z)] Sqrt[I z] + Sqrt[1/z^2] z - Sqrt[(-1 + z)/z] Sqrt[z/(-1 + z)] + Sqrt[1 + 1/z] Sqrt[z/(1 + z)])) - ((2 z)/Sqrt[-1 + z^2]) Sqrt[1 - 1/z^2] ArcCos[1/z]

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2003-08-21