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Algebra Level 3

\[\left( \dfrac { 2\sqrt { 2 } +2\sqrt { 3 } -\sqrt { 5 } }{ 3 } \right) ^{ 2 }+\left( \dfrac { 2\sqrt { 3 } +2\sqrt { 5 } -\sqrt { 2 } }{ 3 } \right) ^{ 2 }+\left( \dfrac { 2\sqrt { 5 } +2\sqrt { 2 } -\sqrt { 3 } }{ 3 } \right) ^{ 2 }= \, ? \]

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