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A10. Triangle with sides in arithmetic sequence.

Find a number n such that there is a triangle with sides n, n + 1, and n + 2 in which the largest angle is twice the smallest angle. How many such numbers n are there? Note that n does not have to be an integer.

This problem came up in a high school textbook during a tutoring session, except there were several hints given that made the problem much easier. See if you can do it without hints.

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