The sum of distinct values of λ for which the system of equations (λ-1) x+(3 λ+1) y+2 λ z=0; (λ-1) x+(4 λ-2) y+(λ+3) z=0; 2 x+(3 λ+1) y+3(λ-1) z=0,…

The sum of distinct values of $\displaystyle \lambda$ for which the system of equations $$\begin{aligned} & (\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0 \\ & (\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0 \\ & 2 x+(3 \lambda+1) y+3(\lambda-1) z=0, \end{aligned} $$ has non-zero solutions, is \_\_\_\_.