\[\sqrt { \left \lfloor x+\left \lfloor \frac { x }{ 2 } \right \rfloor \right \rfloor } +\left \lfloor \sqrt { \{ x\} } +\left \lfloor \frac { x }{ 3 } \right \rfloor \right \rfloor =3\]

Let the solution set of equation above be \([a,b)\) . Find the product, \(a b\).

**Clarification:** \(\{ x\} = x- \lfloor x \rfloor \).

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