Let the system of linear equations
\( x + y + \alpha z = 2 \)
\( 3x + y + z = 4 \)
\( x + 2z = 1 \)
have a unique solution \( (x^*, y^*, z^*) \). If \( (\alpha, x^*) \), \( (y^*, \alpha) \) and \( (x^*, -y^*) \) are collinear points, then the sum of absolute values of all possible values of \( \alpha \) is:
