The remainder when \(x^4 + 3x^2 - 2x + 2\) is divided by \(x + a\) is the square of the remainder when \(x^2 - 3\) is divided by \(x + a\). Calculate the possible values of \(a\).

The remainder when \(x^4 + 3x^2 - 2x + 2\) is divided by \(x + a\) is the square of the remainder when \(x^2 - 3\) is divided by \(x + a\). Calculate the possible values of \(a\).