  We demonstrate equivalence of the in-in formalism and Green's function method
for calculating the bispectrum of primordial gravitational waves generated by
vacuum fluctuations of the metric. The tree-level bispectrum from the field
equation, $B_h$, agrees with the results obtained previously using the in-in
formalism exactly. Characterising non-Gaussianity of the fluctuations using the
ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power
spectrum of scale-invariant gravitational waves, we show that it is much weaker
than in models with spectator gauge fields. We also calculate the tree-level
bispectrum of two right-handed and one left-handed gravitational wave using
Green's function, reproducing the results from in-in formalism, and show that
it can be as large as the bispectrum of three right-handed gravitational waves.
