  Rapid progress in cooling and trapping of molecules has enabled first
experiments on high resolution spectroscopy of trapped diatomic molecules,
promising unprecedented precision. Extending this work to polyatomic molecules
provides unique opportunities due to more complex geometries and additional
internal degrees of freedom. Here, this is achieved by combining a
homogeneous-field microstructured electric trap, rotational transitions with
minimal Stark broadening at a 'magic' offset electric field, and optoelectrical
Sisyphus cooling of molecules to the low millikelvin temperature regime. We
thereby reduce Stark broadening on the $J=5\leftarrow4$ ($K=3$) transition of
formaldehyde at $364\,$GHz to well below $1\,$kHz, observe Doppler-limited
linewidths down to $3.8\,$kHz, and determine the 'magic'-field line position
with an uncertainty below $100\,$Hz. Our approach opens a multitude of
possibilities for investigating diverse polyatomic molecule species.
