= Solution
For a narrowly aligned <nematic liquid crystal>, the scalar <nematic order parameter> is $S=\langle(3\cos^2\theta-1)/2\rangle\simeq1-\frac32\langle\theta^2\rangle$. Hence the <small-angle width of nematic orientation> is
$$
\boxed{\theta_{\rm rms}\simeq\sqrt{\frac{2(1-S)}3}=0.183\,\mathrm{rad}\simeq10.5^\circ.}
$$
This is a root-mean-square angular width about the unoriented <nematic director>. The single value of $S$ does not determine a complete distribution or its full width at half maximum. For an isotropic two-component Gaussian tilt, each transverse component would have standard deviation $\theta_{\rm rms}/\sqrt2$.
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