Vector Algebra

If \(\bar{a}, \bar{b}, \bar{c}\) are three vectors with magnitudes \(\sqrt{3}\), 1, 2 respectively, such that \(\bar{a} \times(\bar{a} \times \bar{c})+3 \bar{b}=\overline{0}\), if \(\theta\) is the angle between \(\bar{a}\) and \(\bar{c}\), then \(\sec ^2 \theta\) is