It can be shown that VC dimension of rotatable rectangles is 7.
The problem is I cannot understand how to approach the solution. So far I used bruteforce to solve this kind of problem, I was drawing points in different shapes and check whenever the hypothesis shatters the points. In this case the heptagon is the key. In solution it's mentioned that it's easy to show that 0,1,2,6,7 points can be shattered, except for bruteforce "drawing" I don't know any other way to show this. And the case with 3 is considered separately.
I would appreciate if someone could explain why case with 0,1,2,6,7 can be shown easily and 3 needs special treating.
Is there are any reason why 8 doesn't work here.