Final answer:
A rat-tail comb is best for design parting, sectioning hair, and opening and removing braids due to its precise parting capability, narrow teeth, and its tapered handle.
Step-by-step explanation:
The type of comb that is excellent for design parting, sectioning large segments of hair, and opening and removing braids is the rat-tail comb.
This comb is characterized by its long, thin handle that tapers to a point, which makes it ideal for creating precise partings in the hair.
The narrow teeth are perfect for detailed styling, while the tail end is useful for sectioning hair and can assist in the process of opening and removing braids without causing damage.