Dr. Antlove loves ants (obviously) and he cannot stand anything happening to his ants. Dr. Rage wants to play with him a little. So he challenges him with a trick puzzle. He gives Dr. Antlove a regular polygon with $628318531$ sides with Queen ant in the middle and gives him a triangular (ant-trap)net that can be tied at any three random vertices of the polygon(any three vertices can be chosen as the vertices of the net at random). But Dr. Antlove is busy with a seminar this weekend. So he orders you to get the ant for him. Before moving on you believe it would be better to calculate the probability of your success. All choices of vertices being equally likely, let the probability that you would be able to catch the ant inside that net be $p$. (All vertices are distinct.)

Give the answer = $p\times2\times$($2\times \lfloor(\pi \times10^8)\rfloor - 1)$