JBMO-SL 2014 A4

Let $a, b, c$ be positive real numbers such that $a+b+c=1$. Prove that

$$\frac{7+2 b}{1+a}+\frac{7+2 c}{1+b}+\frac{7+2 a}{1+c} \geq \frac{69}{4}$$

When does equality hold?