Let S ={ sin^2 2 θ:( sin^4 θ+ cos^4 θ) x^2+( sin 2 θ) x+( sin^6 θ+ cos^6 θ)=0. has real roots }. If α and β be the smallest and largest elements of…

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