Find the reference angle for \( \frac{7 \pi}{9} \). 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 \( \frac{7\pi}{9} \), we first need to determine in which quadrant the angle lies. The angle \( \frac{7\pi}{9} \) is greater than \( \pi \) (which is \( \frac{9\pi}{9} \)) but less than \( \frac{3\pi}{2} \) (which is \( \frac{13.5\pi}{9} \)). Therefore, \( \frac{7\pi}{9} \) is in the second quadrant. The reference angle \( \theta' \) for an angle in the second quadrant can be found using the formula: \[ \theta' = \pi - \theta \] Substituting \( \theta = \frac{7\pi}{9} \): \[ \theta' = \pi - \frac{7\pi}{9} \] To perform the subtraction, we first express \( \pi \) with a common denominator: \[ \pi = \frac{9\pi}{9} \] Now we can subtract: \[ \theta' = \frac{9\pi}{9} - \frac{7\pi}{9} = \frac{2\pi}{9} \] Thus, the reference angle for \( \frac{7\pi}{9} \) is \[ \boxed{\frac{2\pi}{9}} \]