Tricky Equations - 2

Algebra Level 4

$\large \begin{cases} (a+1)(b+1)(c+1)=1 \\ (a+2)(b+2)(c+2)=2 \\ (a+3)(b+3)(c+3)=3 \end{cases}$

Let $$a,b$$ and $$c$$ be complex number satisfying the system of equations above, find $$(a+4)(b+4)(c+4)$$.

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