Let $$S = \{\sin^2 2\theta : (\sin^4 \theta + \cos^4 \theta)x^2 + (\sin 2\theta)x + (\sin^6 \theta + \cos^6 \theta) = 0$$ has real roots$$\}$$. If $$\alpha$$ and $$\beta$$ be the smallest and largest elements of the set $$S$$, respectively, then $$3((\alpha - 2)^2 + (\beta - 1)^2)$$ equals _____