Every Angle for a Tangent

Because tangent repeats every half turn, its angles come in pairs half a turn apart. To list them over an interval, find the first one and keep adding π (or 180°).

Take $\tan\left(\theta\right) = 1$ on [0, 4π). The first angle is π/4. Adding π again and again gives 5π/4, 9π/4 and 13π/4, and the next, 17π/4, is past 4π. Four angles over two turns: two per turn, as with sine and cosine, but evenly spaced.