You can try to find the pdf of (by first finding the pdf of thanks to a Jacobian transformation and then integrating)
Then, you'll get something like for the pdf of Y.
Reverse the integration order (what's in the integral is positive so we can apply Fubini-Tonelli's theorem) and you'll get 0, because you integrate over a set of Lebesgue measure 0.
Otherwise, maybe you can have a look into the properties of convolution... But right now I have to go to school... Good luck !