Let $P_1: \bar{r} .(2 \hat{i}+\hat{j}-3 \hat{k})=4$ 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 $\_\_\_\_$ .