I think you are right: when I changed it from cot^{-1}() to cot()^{-1}it didn't make any difference. I will try it again in a moment. See if it recognises acot().

That fixed it. Thanks. The graph now looks like:

Untitled.jpg

(with y and x instead of alpha and lambda, for values of v = pi/2.2, pi/3, pi/4, pi/6)

Although what it all means ...

There is an odd discontinuity in the curve (I haven't cut it off at y=0 and y=2*pi)