Subacromial Impingement Syndrome: This condition is the most likely diagnosis due to the presence of a painful arc test at 60 degrees, which is indicative of mechanical impingement of the rotator cuff tendons under the acromion. Pain with external rotation also supports this diagnosis, as it can irritate the rotator cuff tendons.

Rotator Cuff Tendinopathy: This condition often presents with pain in the anterior shoulder, especially with movements that involve external rotation. The painful arc test can also be positive in rotator cuff tendinopathy due to inflammation and irritation of the tendons.
Bicipital Tendinopathy: Given the location of the pain (anterior shoulder) and the involvement of external rotation, which can irritate the biceps tendon, bicipital tendinopathy is a plausible diagnosis. However, it might not fully explain the painful arc unless there's associated subacromial impingement.

Fracture (e.g., Humeral Neck Fracture): Although less likely, a fracture could present with acute onset of pain, especially if there was a traumatic event. The painful arc and pain with external rotation could be due to movement at the fracture site.
Infection (e.g., Septic Arthritis or Osteomyelitis): Infections in the shoulder joint or bone can cause severe pain, including pain with movement. While less common, these conditions are critical to diagnose early due to their potential for serious complications.
Axillary Nerve Injury: This could result from trauma or compression and might present with pain and weakness, particularly with external rotation, due to the involvement of the deltoid muscle and teres minor.

Adhesive Capsulitis (Frozen Shoulder): Early stages might present with pain and limited range of motion, but the painful arc test and specific pain with external rotation are less typical for this condition.
Tumors (e.g., Bone or Soft Tissue): Although very rare, tumors could cause shoulder pain and might be considered if other diagnoses are ruled out and the pain persists or worsens over time.