Determination of bearing change between two points (spatial-data)

I am reviewing a paper on transportation mode to understand their methodology (this paper). At some stage, the authors computed the rate of bearing change between the points (GPS points), which happens to be a stumbling block to me, for days, I really can't figure out how they derived the equations.

Specifically, this is how they demonstrated it (illustrating bearing of p2 from p1 from true north).

As usual, papers are not books, so most concepts are assumed to be known by readers, they went ahead to list the following equations, stating...

"The bearing rate is the absolute difference between the bearings of two consecutive points, which are calculated as follows:"

I have been playing around with my little "trigonometry" but I really can't figure out how the equations were derived. Does anyone out there understand this please?

Ah, I landed at the right place, haversine formula. I wish I could save someone's time looking for this.