Answer
$$x = \frac{\pi }{4} + 2n\pi ,\,\,\,n{\text{ is an integer}}$$
Work Step by Step
$$\eqalign{
& \tan x = 1 \cr
& {\text{The equation has solutions }}x = \frac{\pi }{4}{\text{ and }}x = \frac{{5\pi }}{4}{\text{ in the interval}} \cr
& \left[ {0,2\pi } \right).{\text{ Moreover, because }}\tan x{\text{ has a period of }}\pi ,{\text{ there are}} \cr
& {\text{infinitely many other solutions, which can be written as}} \cr
& x = \frac{\pi }{4} + n\pi {\text{ and }}x = \frac{{5\pi }}{4} + n\pi \cr
& {\text{Where }}n{\text{ is an integer}}{\text{.}} \cr
& x = \frac{\pi }{4} + 2n\pi ,\,\,\,n{\text{ is an integer}} \cr} $$
