In your solution, the third segment starts at (cosA, sinA) and needs to cross (0, 0)-(1, 0). From a different view, we could have the third segment start at (1, 0) and needing to cross (0, 0)-(cosA, sinA). We have thus defined two vectors and ask, given each a random direction, what is the probability of these two vectors cross? Does that make sense?