Minimum frequency for unique maximum and minimum of a cosine function

Let $f : [0, 2\pi] \to R,\ f(x) = \cos\left(ax + \frac{\pi}{6}\right)$, where $a > 0$. There is a unique solution to $f(x) = 1$ and a unique solution to $f(x) = -1$.

The minimum possible value of $a$ is