Find all angles, \( 0^{\circ} \leq \theta<360^{\circ} \), that solve the following equation. \[ \tan \theta=1 \]

Solve the equation \( \tan(\theta)=1 \). Solve the equation by following steps: - step0: Solve for \(\theta\): \(\tan\left(\theta \right)=1\) - step1: Find the domain: \(\tan\left(\theta \right)=1,\theta \neq \frac{\pi }{2}+k\pi ,k \in \mathbb{Z}\) - step2: Use the inverse trigonometric function: \(\theta =\arctan\left(1\right)\) - step3: Calculate: \(\theta =\frac{\pi }{4}\) - step4: Add the period: \(\theta =\frac{\pi }{4}+k\pi ,k \in \mathbb{Z}\) - step5: Check if the solution is in the defined range: \(\theta =\frac{\pi }{4}+k\pi ,k \in \mathbb{Z},\theta \neq \frac{\pi }{2}+k\pi ,k \in \mathbb{Z}\) - step6: Find the intersection: \(\theta =\frac{\pi }{4}+k\pi ,k \in \mathbb{Z}\) The angles that solve the equation \( \tan \theta = 1 \) are given by \( \theta = \frac{\pi}{4} + k\pi \), where \( k \) is an integer. Therefore, the angles that satisfy the equation are \( \theta = 45^\circ + 360^\circ k \), where \( k \) is an integer. These angles are in the first quadrant of the unit circle and are the solutions to the equation \( \tan \theta = 1 \) for \( 0^\circ \leq \theta < 360^\circ \).