Question 8 Difficulty: Ill How many solutions, on the interval $] 0,2 \pi[$, are there for the equation, $|\tan \theta|=1$ ? 12 24 36 40

Step 1 ：Find the solutions for the equation \(\tan \theta = 1\) and \(\tan \theta = -1\) in the interval \((0, 2\pi)\)

Step 2 ：\(\tan \theta = 1\) when \(\theta = \frac{\pi}{4} + n\pi\) and \(\tan \theta = -1\) when \(\theta = \frac{3\pi}{4} + n\pi\), where n is an integer

Step 3 ：Find the solutions that fall within the given interval:

Step 4 ：solutions_1 = \(\left[\frac{\pi}{4}, \frac{5\pi}{4}\right]\)

Step 5 ：solutions_2 = \(\left[\frac{3\pi}{4}, \frac{7\pi}{4}\right]\)

Step 6 ：total_solutions = 4

Step 7 ：\(\boxed{4}\) solutions for the equation \(|\tan \theta| = 1\) in the interval \((0, 2\pi)\)