Answer
$\omega_0 = 3.00~rad/s$
Work Step by Step
$\theta = \omega_0 ~t + \frac{1}{2}\alpha ~t^2$
$\omega_0 = \frac{\theta -\frac{1}{2}\alpha ~t^2}{t}$
$\omega_0 = \frac{(30.0~rad) -\frac{1}{2}(2.25~rad/s^2)(4.00~s)^2}{4.00~s}$
$\omega_0 = 3.00~rad/s$
