Mathematics

Problem

If the vectors

\mathbf{a}

and

\mathbf{b}

are linearly independent satisfying

(\sqrt{3} \tan \theta + 1)\mathbf{a} + (\sqrt{3} \sec \theta - 2)\mathbf{b} = \mathbf{0}

, then the most general value of

\theta

are a.

n\pi - \frac{\pi}{6}, n \in \mathbb{Z}

2n\pi \pm \frac{11\pi}{6}, n \in \mathbb{Z}

n\pi \pm \frac{\pi}{6}, n \in \mathbb{Z}

2n\pi + \frac{11\pi}{6}, n \in \mathbb{Z}