Just to make sure you got it
Say the sun was directly overhead the equator at the 0° meridian. To an observer on the equator at 90°E or W, or at either of the poles, the sun would be on the horizon (assuming perfect sphere, no refraction etc etc). To each of the four observers the suns azimuth would be,
South Pole - 000°T
North Pole - 180°T
90°E - 270°T
90°W - 090°T
Each of the four positions lie on a circle, centred at the suns position, of radius 5400NM (assuming 1°=60NM). As the suns altitude increases, as observed by the observer, the radius of the LOP decreases. No matter the radius, unless it's zero, somewhere on the LOP circle the azimuth of the sun will run the full gamut of 360°.
A navigator can even use the sight to determine his compass error.
Had to get out D. C. T. Bennetts "Complete Air Navigator" to make sure I got it as well.