  Known already to the ancient Greeks, today trigonometric identities come in a
large variety of tastes and flavours. In this large family there is a subfamily
of interpolation-like identities discovered by Hermite and revived rather
recently in two independent papers, one by Wenchang Chu and the other by Warren
Johnson exploring various forms and generalizations of Hermite's results. The
goal of this work inspired by these two articles is twofold. The first goal is
to fill a gap in the references from the above papers and exhibit various
trigonometric identities discovered by Meijer, N{\o}rlund and Braaksma between
1940 and 1962 in the context of analytic continuation of Mellin-Barnes
integrals and relations between different solutions of the generalized
hypergeometric differential equation. Our second goal is to present some
extensions of Chu's and Johnson's results by combining them with the ideas of
Meijer and Braaksma adding certain sum manipulations and facts from the complex
analysis. We unify and systematize various known and new identities and
illustrate our results with numerous explicit examples.
