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

To solve the equation \( \tan \theta = 1 \), we first know that the tangent function is equal to one at specific angles on the unit circle. The most common angle is \( 45^\circ \) since the sine and cosine values are equal at that point. However, tangent also has a periodic nature with a period of \( 180^\circ \). So, we can find additional solutions within the specified range by adding \( 180^\circ \) to our initial solution. Starting from \( 45^\circ \): 1. \( \theta = 45^\circ \) 2. Adding the period: \( 45^\circ + 180^\circ = 225^\circ \) Therefore, the angles that solve the equation \( \tan \theta = 1 \) in the range \( 0^{\circ} \leq \theta < 360^{\circ} \) are: \[ \theta = 45^\circ, 225^\circ \]