Within an "area", if you consider any random point, then all the points around it must also be colored, meaning that there must be lines through this point in all possible directions, hence the 0 to 360 degree comment. The problem is similar to the triangle problem where the naked eye tells you that there is a "black area" but infact it is so because you choose the thickness of a point, or a line in this case. If instead of point bouncing off, you had a ball bouncing, I would definitely agree with Bonanova that the complete rectangle can be colored and a 0 white area left off as minimum