Final answer:
Passive external rotation is the optimal positioning of the glenohumeral joint to palpate the greater tuberosity of the humerus.
Step-by-step explanation:
The optimal positioning of the glenohumeral joint to palpate the greater tuberosity of the humerus is passive external rotation. Passive external rotation involves rotating the arm outward away from the body. It allows for better access to the greater tuberosity of the humerus, which is located on the lateral side of the proximal humerus. This positioning is commonly used during physical examinations to assess for shoulder injuries or conditions.