Angle base Sort Polygon Points

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I was working on Scale game: Scale

For this purpose, I require to sort points as per clock wise direction and I implemented algorithm for this process. Here is algorithm reference link: Sort points in clockwise order?

But now this kind of situation occurred for me. I made proper sketch to represent my side error situation. enter image description here

Above figure I hope explaining my problem exactly. Basically using algorithm, points get sorted correctly but as per game requirements, I want some tweak in those.

So what to do in this case? Please give me some suggestion regarding this.

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