尤 and 尤其 both mean "particularly, especially", correct? Then isn't 其 redundant? What role does 其 serve?
Oxford Chinese Dictionary (2010) p 906.
No. As you can see in the dictionary, 尤 must be used with another word, or other words, to form a phrase that means something. For example, it has the meaning of "particular" when used in the phrase "對計算機尤感興趣歐". However, in the phrase "尤物", its meaning changed to "rare", "exceptional".
其, depending on the use, can be translated as "its", "such", "that". Similar to 尤, it must be used with other words to be meaningful. As shown in the dictionary, it means "especially" when in the phrase "尤其重要", and means "particular" in "尤其是綠茶". Thus, the following phrases are false:
尤重要
其重要
尤是綠茶
其是綠茶
尤: yóu means especially, prominent, or especially.
其: qi is a third-person pronoun, equivalent to "he or she".
actually, you'd better remember the phrase as a whole, a lot of characters that already lost their meaning in phrases, explaining them may confuse you. Chinese evolved over the years, there are things that even our Chinese can't explain