Let \(a, b, c\) be positive reals so that \(3ab+bc+2ca=6\). Find the maximum value of

\[\frac { 1 }{ { a }^{ 2 }+1 } +\frac { 4 }{ { b }^{ 2 }+4 } +\frac { 9 }{ { c }^{ 2 }+9 } \]

Write your answer to 4 decimal places.

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