@Markiyan Hirnyk 

Thankyou this was exactly what I meant to do. I came as far as knowing I should use surfdata but I couldn't figure out the rest, now I see why. So thank you!

@Markiyan Hirnyk and @mehdi jafari

Thank you both!
the combination of using fsolve and restricting alfa betwee 0 and 2*pi worked. I feel kind of stupid that I couldn't solve this myself