If \( f(x) \) is a periodic function with period 3 and defind as \( f(x)\left\{\begin{array}{ll}...

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If \( f(x) \) is a periodic function with period 3 and defind as \( f(x)\left\{\begin{array}{ll}\{x\}, & x \in(0,1) \\ {[x],} & x \in(1,2) \\ \{-x\}, & x \in(2,3)\end{array}\right. \) then the value of \( \frac{1}{3} \int_{3}^{12} f(x) d x \) (where [.] and \( \{ \).\( \} denote greatest integer and fractional part \) functions, respetively)
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