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This problem trains for: SAT-II, AMC-12, AMC-10.

Which value is closest to:

equation

The functions tan and arctan are inverses only for angles that are in the principal period of the tan:

equation

Therefore, it would be an error to simply think they satisfy the identity property. The angle 135° is not in the principal period of the tan.

The angle with the same tan(x) value that is in the principal period is:

equation

figure

Therefore:

equation