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For a 3x3 determinant with entries a_ij = arctan(tan(i - j)) for all i, j (i is the row index, j is the column index), find the value of the determinant.

1. 0
2. 1
3. -1
4. 2

Correct answer: 0

Solution

Computing each entry (with arctan(tan 2) = 2 - pi) and expanding the determinant gives exactly 0.

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