Answer
We know, that
$\omega^{2}=\omega_{0}^{2}-2a\Delta\theta$,
let a be the angular acceleration.
i.e. $\Delta\theta=\frac{\omega^{2}-\omega_{0}^{2}}{2a}$
i.e. $\theta-\theta_{0}=\frac{\omega^{2}-\omega_{0}^{2}}{2a}$
i.e. $\theta=\theta_{0}+\frac{\omega^{2}-\omega_{0}^{2}}{2a}$
Work Step by Step
We know, that
$\omega^{2}=\omega_{0}^{2}-2a\Delta\theta$,
let a be the angular acceleration.
i.e. $\Delta\theta=\frac{\omega^{2}-\omega_{0}^{2}}{2a}$
i.e. $\theta-\theta_{0}=\frac{\omega^{2}-\omega_{0}^{2}}{2a}$
i.e. $\theta=\theta_{0}+\frac{\omega^{2}-\omega_{0}^{2}}{2a}$