1. Let $P$ and $Q$ be any two points on the curve
$$
y=x^{3}-3 x^{2}+(3-\sqrt{3}) x+\frac{3}{4}
$$

Then the range of the inclination angle $\alpha$ of the line $PQ$ is $\qquad$
二、1. $\left[0, \frac{\pi}{2}\right) \cup\left(\frac{2 \pi}{3}, \pi\right)$.
Finding the derivative, we know that the slope $k \geqslant -\sqrt{3}$ of the tangent line at any point on the curve. Therefore, the slope of the line passing through any two different points on the curve is greater than $-\sqrt{3}$. Thus, the range of the inclination angle of the line $P Q$ is $\left[0, \frac{\pi}{2}\right) \cup\left(\frac{2 \pi}{3}, \pi\right)$.