Find the reference angle for \( \frac{7 \pi}{6} \), The reference angle is (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in radians.)

To find the reference angle for \( \frac{7\pi}{6} \), we first need to determine in which quadrant the angle lies. The angle \( \frac{7\pi}{6} \) is greater than \( \pi \) (which is \( \frac{6\pi}{6} \)) and less than \( \frac{3\pi}{2} \) (which is \( \frac{9\pi}{6} \)), so it is in the third quadrant. The reference angle \( \theta_{\text{ref}} \) for an angle in the third quadrant can be found using the formula: \[ \theta_{\text{ref}} = \theta - \pi \] Substituting \( \theta = \frac{7\pi}{6} \): \[ \theta_{\text{ref}} = \frac{7\pi}{6} - \pi \] To perform the subtraction, we convert \( \pi \) to sixths: \[ \pi = \frac{6\pi}{6} \] Now we can subtract: \[ \theta_{\text{ref}} = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{1\pi}{6} = \frac{\pi}{6} \] Thus, the reference angle for \( \frac{7\pi}{6} \) is \[ \boxed{\frac{\pi}{6}} \]