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

$\left( {\lambda - 1} \right)x + \left( {3\lambda + 1} \right)y + 2\lambda z = 0$
$\left( {\lambda - 1} \right)x + \left( {4\lambda - 2} \right)y + \left( {\lambda + 3} \right)z = 0$
$2x + \left( {3\lambda + 1} \right)y + 3\left( {\lambda - 1} \right)z = 0$

has non-zero solutions, is ________ .