Determine the numerical value of the following expression without the use of a calculator:

[tex] log( log(3) \times ( log(2) \times ( \frac{ \sqrt{3} - 2 \sin( \frac{x}{3} ) }{ {x}^{3} + 1} + 1)) - log(2) log(3) + ( { - 1}^{100} ) ) [/tex]
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