Solution (source code)

= Solution

With integer fluorine mass $m_B=19m_{\rm u}$ and $R=1.5\ \mathring{\mathrm A}$,
$$
\cos\theta=1-\frac{146.588}{4(19)(1.5)^2}=0.14276,
\qquad\boxed{\theta\simeq81.8^\circ.}
$$
This angle is below the planar limit $90^\circ$, consistent with the proposed pyramid. The sulfur mass does not enter this axial <moment of inertia>.