$\displaystyle a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1.$

Then prove that

$\displaystyle \left( a+\dfrac{1}{b}\right).\left(b+\dfrac{1}{c}\right). \left(c+\dfrac{1}{a}\right)\geq \left(\dfrac{10}{3}\right)^3$

Anyone an idea on how to start with this exercise?