Analysis We are asked to solve the given trigonometric equation for $\theta$ in the interval $\left[0^{\circ}, 360^{\circ} ight)$. The equation involves the tangent function. We will first isolate the tangent function and then use the inverse tangent function to find the reference angle. Since the tangent function is positive in the first and third quadrants, we will find the solutions in those quadrants. Step 1 Isolate the tangent function: \[ \tan (\theta) = 2.6 \cdot \frac{7}{8.3} = \frac{18.2}{8.3} \approx 2.19277 \] Step 2 Find the reference angle by taking the inverse tangent of the positive value: \[ \theta_{ref} = \arctan\left(\frac{18.2}{8.3} ight) \approx 65.4815^{\circ} \] Step 3 Since the tangent function is positive in the first and third quadrants, we find the solutions in those quadrants. In the first quadrant: \[ \theta_1 = \theta_{ref} \approx 65.4815^{\circ} \] In the third quadrant: \[ \theta_2 = 180^{\circ} + \theta_{ref} \approx 180^{\circ} + 65.4815^{\circ} = 245.4815^{\circ} \] Step 4 Round the solutions to four decimal places: \[ \theta_1 \approx 65.4815^{\circ} \] \[ \theta_2 \approx 245.4815^{\circ} \] Answer $\theta=65.4815^{\circ}, 245.4815^{\circ}$ Round up the answer to 4 decimals places