Probability of absolute sum of discrete variables

Let $(X, Y)$ be a random vector having the joint moment generating function $$M(t_1, t_2)=\left(\frac{1}{2}e^{-t_1}+\frac{1}{2}e^{t_1}\right)^2 \left(\frac{1}{2}+\frac{1}{2}e^{t_2}\right)^2,\quad (t_1, t_2)\in\mathbb{R}^2.$$ Then $P(|X+Y|=2)$ equals __________ (round off to $2$ decimal places)