Find Ant Collisions

There are three ants on different vertices of a triangle. What is the probability of colli­sion (between any two or all of them) if they start walking on the sides of the triangle?

Similarly, find the probability of collision with ‘n’ ants on an ‘n’ vertex polygon.

The solution will be disclosed within x week.

$x$ is $\sin ^230$ °$-\tan 45$ °$+\sin ^260$ °$+ \tan30$° $\tan60$°