Let \( P_1 : \vec{r} \cdot (2\vec{i} + \vec{j} - 3\vec{k}) = 4 \) be a plane. Let \( P_2 \) be another plane which passes through the points \( (2, -3, 2) \), \( (2, -2, -3) \) and \( (1, -4, 2) \). If the direction ratios of the line of intersection of \( P_1 \) and \( P_2 \) be \( 16, \alpha, \beta \), then the value of \( \alpha + \beta \) is equal to _________.
