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]