The angles of a triangle, two of whose sides are represented by the vectors \[\sqrt{3}(\vec{a}\times \vec{b})\] and \[\vec{b}-(\vec{a}.\vec{b})\vec{a}\] where \[\vec{b}\] is a non-zero vector and \[\vec{a}\]is a unit vector are

• A. \[\tan {{\,}^{-1}}\left( \frac{1}{\sqrt{3}} \right);\,\tan {{\,}^{-1}}\left( \frac{1}{2} \right);\,\tan {{\,}^{-1}}\left( \frac{\sqrt{3}+2}{1-2\sqrt{3}} \right)\]
• B. \[\tan {{\,}^{-1}}\left( \sqrt{3} \right);\,\tan {{\,}^{-1}}\left( \frac{1}{\sqrt{3}} \right);\,\cot {{\,}^{-1}}\left( 0 \right)\]
• C. \[\tan {{\,}^{-1}}\left( \sqrt{3} \right);\,\tan {{\,}^{-1}}\left( 2 \right);\,\tan {{\,}^{-1}}\left( \frac{\sqrt{3}+2}{2\sqrt{3}-1} \right)\]
• D. \[\tan {{\,}^{-1}}\left( \sqrt{3} \right);\,\tan {{\,}^{-1}}\left( \sqrt{2} \right);\,\tan {{\,}^{-1}}\left( \frac{\sqrt{2}+3}{3\sqrt{2}-1} \right)\]