Why I always WA on text 2?

If you sort points by angle from Wally's home, there is one tricky case - when angle difference between two sequential points is greater than PI.

For example if angle range is [-PI; PI]:
0 0
3
-1 -1 1
0 1 2
-1 1 3
Program that sort angles will output
0
1
2
3
0
and it is wrong, 1-2 will intersect with 3-0.

Text for angle range [0; 2PI] is
0 0
3
1 1 1
0 -1 2
1 -1 3
Again sorting program will output
0
1
2
3
0
and again it is wrong, 1-2 will intersect with 3-0.

Hint: after sorting there may be not more than one pair of sequential points with angle difference greater than PI.

Thanks for the hint!