A technique will solve this easily

Algebra Level 2

\[\large \dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}+\dfrac{2(a^2+b^2+c^2)}{3}\] Let \(a,b\) and \(c\) be positive reals satisfy \(a+b+c=3\). Find the minimum value of the expression above.

Give your answer to 2 decimal places

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