Step 1: Recognise painful arc syndrome as subacromial impingement, where soft tissue is pinched between the humeral head and the acromion during arm elevation.
Step 2: Map the painful range - symptoms appear over the middle portion of abduction, roughly $60^\circ$ to $120^\circ$, where the inflamed supraspinatus passes under the coracoacromial arch.
Step 3: Below $60^\circ$ and above $120^\circ$ the tendon clears the arch, so the extremes of motion are relatively painless, which is why initial, full, and overhead abduction are wrong.
Step 4: The pain therefore localises to the mid arc of abduction.
\[\boxed{\text{Mid abduction (60-120 degrees)}}\]