For the curve $x=3 \cos \theta, y=3 \sin \theta$, $0 \leq \theta \leq \pi$, the tangent is parallel to the x-axis, where $\theta=$

$\frac{\pi}{2}$

For the tangent to be parallel to x-axis, we must have

$\frac{d y}{d x}=0 \Rightarrow \frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}}=0 \Rightarrow \frac{3 \cos \theta}{-3 \sin \theta}=0 \Rightarrow \cot \theta=0 \Rightarrow \theta=\frac{\pi}{2}$