CN-SMO 2009 Problem 7

Let $x,y,z\geq0$ be real numbers such that $x+y+z=1$ Define $f(x,y,z)$ in this way : $$f(x,y,z)=\frac{x(2y-z)}{1+x+3y}+\frac{y(2z-x)}{1+y+3z}+\frac{z(2x-y)}{1+z+3x}$$ Find the minimum value and maximum value of $f(x,y,z)$ .