Question: How to remove discontinuity in plot3d?

plot3d([arctan(-tan(u/4)) + ((cosh(v) - sinh(v))*sin(u))/2, -v/2 + ((cosh(v) - sinh(v))*cos(u))/2, 2*(cosh(v/2) - sinh(v/2))*sin(u/2)], u = 0 .. 6*Pi, v = -1 .. 1, grid = [80, 15], orientation = [50, 79], shading = XYZ, style = patch)

I started to draw minimal surfaces in Maple and I noticed a problem with the parameterization of the function. When I have piecwise function like this arctan(-tan(u/4)) which graph I sent below the 3dplot shows this discontinuity. If it was only 2dplot I could use discont in the code but here I don't see a good solution.

I found these two posts but I can't translate it into a problem with the given parameterization, thank you for all advise.

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