Calculating circulation around a latitude circle

Hello,
            It probably is  a very trivial question but I think (and hope)
that there is no harm in asking for  a clarification. I have grid
coordinates and their  associated velocities arranged along a latitude
circle(https://en.wikipedia.org/wiki/Circle_of_latitude_ . I am wanting to
calculate the circulation around that latitude circle.  I have seen this
example -
http://www.joshtheengineer.com/2019/04/01/compute-circulation-of-a-vector-field-in-matlab-and-python/
and the associated video - https://www.youtube.com/watch?v=b8EnhiSjL3o .
But I think my case is a trivial case of what is being  explained  in those
links. A straightforward application of Stokes integral in my case as shown
below

Numerical integration of (u_i d (lambda) + v . (d theta)). In my case
d.theta is zero since there is no change of latitude along a latitude
circle . Am I right on those assumptions ? Or do I need to interpolate my
grid coordinates to an ellipse as shown in that example ?

Thanks and regards,
Ashwin.

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