Let the arc \( AC \) of a circle subtend a right angle at the centre \( O \). If the point \( B \) on the arc \( AC \), divides the arc \( AC \) such that \( \frac{\text{length of arc } AB}{\text{length of arc } BC} = \frac{1}{5} \), and \( \overrightarrow{OC} = \alpha\overrightarrow{OA} + \beta\overrightarrow{OB} \), then \( \alpha + \sqrt{2(\sqrt{3} - 1)}\beta \) is equal to \begin{align*}