How to rotate a vector by angle if you have angle between the $\beta$ vector and the $\alpha$ vector?

Question

I am trying to rotate $\alpha$ vector CLOCKWISE so that is aligned with $\beta$ vector. I know the angle between them is $\theta = 60^⚬$. Both the magnitude of the vectors is 1.

$\begin{equation*} \alpha = \begin{pmatrix}0.866\\0.5\end{pmatrix} \end{equation*}$

$\begin{equation*} \beta = ? \end{equation*}$

$\begin{equation*} \theta = 60^⚬ \end{equation*}$

How can I find the vector $\beta$. If I know the angle between the vectors?