Let \( f(x)=\left([a]^{2}-5[a]+4\right) x^{3}-\left(6\{a\}^{2}-5\{a\}+1\right) x-(\tan x) \) \( ...

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Let \( f(x)=\left([a]^{2}-5[a]+4\right) x^{3}-\left(6\{a\}^{2}-5\{a\}+1\right) x-(\tan x) \) \( \times \operatorname{sgn} x \) be an even function for all \( x \in R \). Then the sum of all possible values of \( a \) is (where [.] and \( \{\cdot\} \) denote greatest integer function and fractional part function, respectively)
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