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 __________.
