It is given that \(\frac{2 + 3ai}{a + 2i} = \lambda(2 - i)\), where \(a\) and \(\lambda\) are real constants.

(a) Show that \(3a^2 + 4a - 4 = 0\).

(b) Hence find the possible values of \(a\) and the corresponding values of \(\lambda\).