1. **State the problem:** Find the related acute angle of $\frac{14\pi}{3}$. Related acute angle means the smallest positive angle between the terminal side of the given angle and the x-axis. 2. **Formula and rules:** To find the related acute angle, first reduce the angle to an equivalent angle between $0$ and $2\pi$ by subtracting multiples of $2\pi$. 3. **Calculate equivalent angle:** $$\frac{14\pi}{3} - 4 \times 2\pi = \frac{14\pi}{3} - \frac{24\pi}{3} = -\frac{10\pi}{3}$$ Since this is negative, add $2\pi$ until positive: $$-\frac{10\pi}{3} + 4 \times 2\pi = -\frac{10\pi}{3} + \frac{24\pi}{3} = \frac{14\pi}{3}$$ This cycles back, so better to reduce directly: $$\frac{14\pi}{3} = 4\pi + \frac{2\pi}{3}$$ Since $4\pi$ is two full rotations, the equivalent angle is: $$\frac{2\pi}{3}$$ 4. **Find related acute angle:** The angle $\frac{2\pi}{3}$ is in the second quadrant. The related acute angle $\alpha$ is: $$\alpha = \pi - \frac{2\pi}{3} = \frac{\pi}{3}$$ 5. **Answer:** The related acute angle is $\frac{\pi}{3}$. **Final answer:** a) $\frac{\pi}{3}$