XK-TST 2015 Problem 4

Let $P_1,P_2,...,P_{2556}$ be distinct points inside a regular hexagon $ABCDEF$ of side $1$ . If any three points from the set $S=\{A,B,C,D,E,F,P_1,P_2...,P_{2556}\}$ aren't collinear, prove that there exists a triangle with area smaller than $\frac{1}{1700}$ , with vertices from the set $S$ .