Tangent's Single Family

$\tan\left(x\right) = 1$ has 45° and 225° in one turn. Those two are 180° apart, and tangent repeats every 180°, so one family covers both:

$$x = 45^{\circ}+180^{\circ}\cdot k$$

k = 1 gives 225°, k = 2 gives 405°. Writing 45° + 360°k loses every other answer, the most common slip with tangent. Use the period of the function: 360° for sine and cosine, 180° for tangent.