In circle $O, \mathrm{~m} \angle P O Q=40^{\circ}$ and the length of $P Q=\frac{2}{3} \pi$. Find the length of $\overline{O P}$.

Step 1 ：Convert the given angle from degrees to radians: \(angle_in_radians = \frac{angle_in_degrees * \pi}{180}\)

Step 2 ：\(angle_in_radians = \frac{40 * \pi}{180} = 0.6981317007977318\)

Step 3 ：Use the rearranged arc length formula to find the length of the radius $OP$: \(radius = \frac{arc_length}{angle_in_radians}\)

Step 4 ：\(radius = \frac{\frac{2}{3} \pi}{0.6981317007977318} = 3.0\)

Step 5 ：\(\boxed{3.0}\)