Real numbers \( a, b, c \) satisfy the following conditions: \[ 1000 < |a| < 2000, \quad 1000 < |b| < 2000, \quad 1000 < |c| < 2000, \]and \[ \frac{ab^2}{a+b} + \frac{bc^2}{b+c} + \frac{ca^2}{c+a} = 0. \]What are the possible values of the expression \[ \frac{a}{b} + \frac{b}{c} + \frac{c}{a}? \] Proposed by Vadym Solomka