Let $a$ be a complex number, and set $\alpha$, $\beta$, and $\gamma$ to be the roots of the polynomial $x^3 - x^2 + ax - 1$. Suppose $$(\alpha^3+1)(\beta^3+1)(\gamma^3+1) = 2018.$$ Compute the product of all possible values of $a$.

Let's think step by step and output the final answer within \boxed{}.
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