Vector Algebra

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