1. The problem is to solve the equation $$\frac{\cos 3x}{2} = 0$$ for $x$. 2. First, multiply both sides by 2 to eliminate the denominator: $$\cos 3x = 0$$ 3. Recall that $\cos \theta = 0$ at angles $\theta = \frac{\pi}{2} + k\pi$, where $k$ is any integer. 4. Set $3x = \frac{\pi}{2} + k\pi$: $$3x = \frac{\pi}{2} + k\pi$$ 5. Solve for $x$ by dividing both sides by 3: $$x = \frac{\pi}{6} + \frac{k\pi}{3}$$ 6. Therefore, the general solution is: $$x = \frac{\pi}{6} + \frac{k\pi}{3}, \quad k \in \mathbb{Z}$$ This means $x$ takes values starting at $\frac{\pi}{6}$ and increases by $\frac{\pi}{3}$ for each integer $k$. Final answer: $$x = \frac{\pi}{6} + \frac{k\pi}{3}, \quad k \in \mathbb{Z}$$