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Here is a way to do it
This code will find the angle of a given point for the selected spline obj. At the top of the code you can input which point in the spline you'd like to calculate the angle for, if no point is specified all points in the spline will be calculated. Make sure to select a spline before running the script. I used the cosine rule to get the angle.
Hope this helps,
-Maarten
Working on it :)
I'm writing some code atm, trying to figure it out will get back to you as soon as I have it done :)