If you are dealing with both genders, you simply say, "Everyone took his or her coat off the rack." It is a rule that confuses many people, and in everyday language, most people do just say, "Everyone took their coat." The problem is that we don't have a singular, gender-free pronoun to use, so this rule is weird. You can also avoid the gender thing by taking out the possessive: "Someone took a coat off the rack/Everyone took a coat off the rack." That way you don't trip up on gender or singular vs. plural. The English language is so weird, but I can assure you as a certified English teacher that this weird-ass rule is correct.