If the value of \(\frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ}\) is \(\frac{\alpha + \beta\sqrt{5}}{\gamma}\) then value of \((\alpha + \beta + \gamma)\) (where \(\alpha, \beta, \gamma \in \mathbb{N}\) and are in lowest form) :