Answer
$6.8rad/s$
Work Step by Step
We know that
$\Delta \theta=2\frac{1}{2}rev$
$\implies \Delta \theta=2.5rev$
Now $\omega=\frac{\Delta \theta}{t}$
We plug in the known values to obtain:
$\omega=\frac{2.5rev}{2.3s}$
$\implies \omega=1.0869rev/s$
$\implies \omega=(1.0869rev/s)(\frac{2\pi \space rad}{1rev})$
$\omega=6.8rad/s$