Answer
$$(-\frac{\pi }{4}, \frac{3\pi }{4}), \\ -\frac{\pi }{4}, \\ \frac{3\pi }{4}$$
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:$$0 \lt x+\frac{\pi }{4} \lt \pi \quad \Rightarrow \quad -\frac{\pi }{4} \lt x \lt \frac{3\pi }{4}$$
