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