a ArcTan[x] + b ArcTanh[y] == a Pi Floor[(-Arg[1 - I x] + Arg[I x + 1] + Pi)/(2 Pi)] - 2 I Pi (Floor[(-Arg[((1 - I x)/(I x + 1))^((I a)/2)/(1 - y)^(b/2)] - Arg[(y + 1)^(b/2)] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[((1 - I x)/(I x + 1))^((I a)/2)/(1 - y)^(b/2)]])/ (2 Pi)] + Floor[(Pi - (1/2) Im[b Log[y + 1]])/(2 Pi)]) - 2 I Pi (Floor[(-Arg[((1 - I x)/(I x + 1))^((I a)/2)] - Arg[(1 - y)^(-(b/2))] + Pi)/(2 Pi)] + Floor[((1/2) Im[b Log[1 - y]] + Pi)/(2 Pi)] + Floor[(Pi - (1/2) Re[a Log[(1 - I x)/(I x + 1)]])/(2 Pi)]) + I Pi (1 - (-1)^Floor[Arg[((y + 1)^(b/2) ((1 - I x)/(I x + 1))^((I a)/2))/ (1 - y)^(b/2) + 1]/(2 Pi) + 1/2]) + 2 I ArcTan[(I (1 - (((1 - I x)/(I x + 1))^((I a)/2) (y + 1)^(b/2))/ (1 - y)^(b/2)))/(((y + 1)^(b/2) ((1 - I x)/(I x + 1))^((I a)/2))/ (1 - y)^(b/2) + 1)]

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