Answer
$$(0, \pi ), \\ 0, \\ \pi $$
Work Step by Step
Please note that in order to find the interval containing one period and the two consecutive asymptotes, we need to solve the following inequality:$$-\frac{\pi }{2} \lt x-\frac{\pi }{2} \lt \frac{\pi }{2} \quad \Rightarrow \quad 0 \lt x \lt \pi $$
