A point moves along the curve $y = \sqrt{1 - x^2}$ for $x \in [0, 1]$. Let $\theta$ be the angle such that $x = \sin(\theta)$. If the point moves such that $\theta$ increases at a constant rate of $0.5$ rad/s, find the rate of change of the $x$-coordinate when $\theta = \pi/6$.