  Applying the triplicate form of the extended Gould--Hsu inverse series
relations to Dougall's summation theorem for the well--poised $_7F_6$-series,
we establish, from the dual series, several interesting Ramanujan--like
infinite series expressions for $\pi^2$ and $\pi^{\pm1}$ with convergence rate
"$-\frac{1}{27}$".
