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].