\[{{L}_{1}}\] and \[{{L}_{2}}\] are two lines whose vector equations are \[{{L}_{1}}:\overset{\to }{\mathop{r}}\,=\lambda ((cos\,\,\theta +\sqrt{3})\hat{i}+(\sqrt{2}sin\,\,\theta )\hat{j}\]\[+(cos\theta -\sqrt{3})\hat{k}){{L}_{2}}:\overset{\to }{\mathop{r}}\,=\mu \left( a\hat{i}+b\hat{j}+c\hat{k} \right)\], where \[\lambda \] and \[\mu \] are scalars and \[\alpha \] is the acute angle between \[{{L}_{1}}\] and\[{{L}_{2}}\]. If the angle \['\alpha '\] is independent of \[\theta \] then the value of \['\alpha '\] is

• A. \[\frac{\pi }{6}\]
• B. \[\frac{\pi }{4}\]
• C. \[\frac{\pi }{3}\]
• D. \[\frac{\pi }{2}\]