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The roots of the polynomial equation $x^3 + 2 x^2 + 3 x + 4 = 0$ are $\alpha, \beta,$ and $\gamma$. What is the value of

$\frac{ \alpha + \beta} { \gamma} + \frac{ \beta + \gamma} { \alpha } + \frac{ \gamma + \alpha } { \beta } ?$

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