Let a line passing through the point (-1,2,3) intersect the lines L_1: (x-1)/3=(y-2)/2=(z+1)/-2 at M(α, β, γ) and L_2: (x+2)/-3=(y-2)/-2=(z-1)/4 at…

Let a line passing through the point $\displaystyle (-1,2,3)$ intersect the lines $\displaystyle L_1: \frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}$ at $\displaystyle M(\alpha, \beta, \gamma)$ and $\displaystyle L_2: \frac{x+2}{-3}=\frac{y-2}{-2}=\frac{z-1}{4}$ at $\displaystyle N(a, b, c)$. Then, the value of $\displaystyle \frac{(\alpha+\beta+\gamma)^2}{(a+b+c)^2}$ equals $\displaystyle \_\_\_\_$.