The sum of all the angles θ with 0° < θ < 180° for which tan3θ = 1 is:

As θ runs over 0° to 180°, the tripled angle 3θ runs over 0° to 540°, and the tangent equals 1 at 45°, 225° and 405° in that stretch — three values, not one, because the tangent repeats every 180°. Dividing by 3 gives θ = 15°, 75° and 135°, all inside the stated range, and their sum is 225°. Each checks: tan45° = tan225° = tan405° = 1. Stopping at the first solution gives 15°, forgetting the third gives 15° + 75° = 90°, and quoting only the largest solution gives 135°.