Answer
General formula for solutions: $\dfrac{\pi}{4}+k\pi$, where $k$ is an integer
Six solutions: $\left\{\dfrac{\pi}{4}, \dfrac{5\pi}{4}\pi, \dfrac{9\pi}{4}, \dfrac{13\pi}{4}, \dfrac{17\pi}{4}, \dfrac{21\pi}{4}\right\}$
Work Step by Step
$\tan\theta=1$
Since the period of tangent is $\pi$, then the solutions are:
$\theta=\frac{1}{4}\pi+k\pi$ where $k$ is an integer
Six possible solutions are:
$k=0$
$\theta=\frac{1}{4}\pi+(0)\pi=\frac{1}{4}\pi$
$k=1$
$\theta=\frac{1}{4}\pi+(1)\pi=\frac{5}{4}\pi$
$k=2$
$\theta=\frac{1}{4}\pi+(2)\pi=\frac{9}{4}\pi$
$k=3$
$\theta=\frac{1}{4}\pi+3\pi=\frac{13}{4}\pi$
$k=4$
$\theta=\frac{1}{4}\pi+4\pi=\frac{17}{4}\pi$
$k=5$
$\theta=\frac{1}{4}\pi+(5)\pi=\frac{21}{4}\pi$
