Can You Prove This Inequality for Positive Real Numbers a,b,c,d with Sum of 1?

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

Then prove that

\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?
 
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wnvl said:
a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1.

implies 0<a+b+c<1
 

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