In general, do not capitalize the word the before proper nouns. Examples: ... In special cases, if the word the is an inseparable part of something's official title, it may be capitalized.

Is the capitalized in a proper noun?

Only the first word and important words of a title are capitalized. Prepositions (of, on, for, in, to, with, etc.) and articles (a, an, the) are not capitalized unless they are the first word of a title (“A Tale of Two Cities,” “Of Mice and Men,” “The New York Times”).

Is the capitalized in the middle of a title?

In all three styles, you should not capitalize articles in the title unless they are the first or last word in the title. Articles include "the," "a," and "an," as you can see here: Through the Looking Glass.