Why are the stars of the constellation the Sun currently occupies completely invisible during the day?
Answer
They are washed out by the Sun's brightness
The fundamental reason one cannot observe the constellation the Sun is currently passing through during the daytime is due to the overwhelming luminance of our local star. The Sun illuminates the sky so intensely that the comparatively faint light emanating from the background stars, even those belonging to the constellation currently intersected by the ecliptic, is completely obscured. Essentially, the intense solar glare overpowers the weak stellar light, making visual detection of the occupied constellation impossible until the Sun has set below the horizon, allowing the night sky to become visible.

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