\[\large{\Re \bigg(\text{Li}_3(1 - i)\bigg)= \frac{\pi^a}{b} \ln(2) + \frac{c}{d} \zeta(e)}\]

If the equation above is true for constants \(a,b,c,d\) and \(e,\) find the value of \(a+b+c+d+e\).

This is part of Ordered Disorder.

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