JBMO 2009 Problem 3

Let $x$ , $y$ , $z$ be real numbers such that $0 < x,y,z < 1$ and $xyz = (1 - x)(1 - y)(1 - z)$ . Show that at least one of the numbers $(1 - x)y,(1 - y)z,(1 - z)x$ is greater than or equal to $\frac {1}{4}$