HMMT 2015 T1

The complex numbers $x, y, z$ satisfy

$\begin{aligned} x y z & =-4 \\ (x+1)(y+1)(z+1) & =7 \\ (x+2)(y+2)(z+2) & =-3 \end{aligned}$

Find, with proof, the value of $(x+3)(y+3)(z+3)$ .

Dataset text NuminaMath olympiads. Quoted with source.

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