  We report the results of a detailed study of the field orientation-dependence
of the de Haas-van Alphen waveform in $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$. By
considering the field orientation-dependence of the sign and phase of the
fundamental $\alpha$ frequency, at fields both well above and below the kink
transition field, it is found that a single value for the product of the
effective mass with the electron {\it g}-factor can explain the experimental
data deep within both the high magnetic field and low magnetic field phases.
This implies that spin-splitting does not occur within the low magnetic field
phase until the angle between the magnetic field and the normal to the
conducting planes is $\sim$~42$^\circ$. This finding contrasts greatly with
that recently published by Sasaki and Fukase, implying that electron-electron
interactions do not play a significant role in the formation of the
charge-density wave ground state. The manner in which the amplitude of the
waveform of the oscillations is damped within the low magnetic field phase is
indicative of a non harmonically indexed reduction of the amplitude, thereby
eliminating both magnetic breakdown and impurity scattering as dominant damping
mechanisms within this phase. Meanwhile, the presence of a large amplitude
second harmonic within the low magnetic field phase that has a negative sign
over a broad range of angles can only be explained by the frequency doubling
effect.
