A Nice Inequality

Algebra Level 4

\[\large \dfrac{1}{2a+b}+\dfrac{1}{2b+c}+\dfrac{1}{2c+a}\] If \(a,b\) and \( c\) are positive reals satisfying \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\), find the maximum value of the expression above.

Submit your answer to 3 decimal places