Trigonometric Functions And Equations

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