Consider a sequence of Euler rotations represented by
$$
\begin{aligned}
\mathscr{D}^{(1 / 2)}(\alpha, \beta, \gamma) &=\exp \left(\frac{-i \sigma_{3} \alpha}{2}\right) \exp \left(\frac{-i \sigma_{2} \beta}{2}\right) \exp \left(\frac{-i \sigma_{3} \gamma}{2}\right) \\
&=\left(\begin{array}{cc}
e^{-i(a+\gamma) / 2} \cos \frac{\beta}{2} & -e^{-i(a-\gamma) / 2} \sin \frac{\beta}{2} \\
e^{i(\alpha-\gamma) / 2} \sin \frac{\beta}{2} & e^{i(\alpha+\gamma) / 2} \cos \frac{\beta}{2}
\end{array}\right)
\end{aligned}
$$
Because of the group properties of rotations, we expect that this sequence of operations is equivalent to a single rotation about some axis by an angle $\theta$. Find $\theta$.