Show there is a constant $C$ such that the following holds: For every $0<\epsilon<0.1$ and for every probability measure $\mu$ on the square $[0,1]^2$, if $X$ is a random set of $C/\epsilon \log(1/\epsilon)$ points chosen randomly and independently according to $\mu$, then with probability at least $0.9$ for every two triangles $T_1, T_2$ in $[0,1]^2$ satisfying $\mu(T_1 \setminus T_2)>\epsilon, X \cap T_1 \neq X \cap T_2$.
I am trying to show the set of $C/\epsilon \log(1/ \epsilon)$ points is an $\epsilon$-net with range $T_1 \setminus T_2$, but wasn't sure how to calculate the VC dimension of set of $T_i \setminus T_j$.