ILL 1990 Problem 88

Let $w, x, y, z$ are non-negative reals such that $wx + xy + yz + zw = 1$. Show that $\frac {w^3}{x + y + z} + \frac {x^3}{w + y + z} + \frac {y^3}{w + x + z} + \frac {z^3}{w + x + y}\geq \frac {1}{3}$.