Squares

Algebra Level 3

$\large \bigg(\frac{a}{a+2b}\bigg)^2+\bigg(\frac{b}{b+2c}\bigg)^2+\bigg(\frac{c}{c+2a}\bigg)^2$

If $a,b$ and $c$ are positive reals, find the minimum value of the expression above to 2 decimal places.