Prove that $0 \le xy+yz+xz - 2xyz \le 7/27, \:\:\:x,y,z \ge 0$ with $x+y+z=1$.
IMO 1984: Prove that $0 ≤ yz + zx +xy −2xyz ≤ \frac {7}{27}$, where $x,y$ and $z$ are non-negative real numbers for which $x + y + z = 1.$