In triangle $XYZ,$ $\angle Y = 45^\circ$ and $\angle Z = 60^\circ.$ If $XZ = 4,$ then what is $XY$? [asy]
unitsize(3 cm);

pair X, Y, Z;

X = (0,1);
Y = (-1,0);
Z = (1/sqrt(3),0);

draw(X--Y--Z--cycle);

label("$45^\circ$", Y + (0.3,0.1), fontsize(10));
label("$60^\circ$", Z + (-0.2,0.1), fontsize(10));
label("$X$", X, N);
label("$Y$", Y, SW);
label("$Z$", Z, SE);
label("$4$", (X + Z)/2, NE);
[/asy]