INMO 1991 Problem 4

Let $a,b,c$ be real numbers with $0 < a< 1$ , $0 < b < 1$ , $0 < c < 1$ , and $a+b + c = 2$ . Prove that $\dfrac{a}{1-a} \cdot \dfrac{b}{1-b} \cdot \dfrac{c}{1-c} \geq 8$ .