Let a and b be two vectors such that | a |=1,| b |=4, and a · b =2. If c =(2 a × b )-3 b and the angle between b and c is α, then 192 sin^2 α is…

Let $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ be two vectors such that $\displaystyle |\vec{a}|=1,|\vec{b}|=4$, and $\displaystyle \vec{a} \cdot \vec{b}=2$. If $\displaystyle \vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$ and the angle between $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$ is $\displaystyle \alpha$, then $\displaystyle 192 \sin ^2 \alpha$ is equal to $\displaystyle \_\_\_\_$