The sum of distinct values of \( \lambda \) for which the system of equations \( (\lambda-1) x+(3 \lambda+1) y+2 \lambda…

The sum of distinct values of \( \lambda \) for which the system of equations

\( (\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0 \)

\( (\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0 \)

\( 2 \mathrm{x}+(3 \lambda+1) \mathrm{y}+3(\lambda-1) \mathrm{z}=0 \),

has non-zero solutions, is.............

[JEE Main 2020, 6 Sep (Shift 2)]