  In this paper, we obtain a generalization, in dimension $3$, of a theorem of
David Rees about joint reductions of the bigraded filtration $\{
\overline{I^rJ^s}\}$ of complete ${\mathfrak m}$-primary ideals and vanishing
of the second normal Hilbert coefficient $\overline{e}_2(IJ)$ where $R$ is a
two-dimensional Cohen-Macaulay analytically unramified local ring with maximal
ideal $\mathfrak m.$ This generalization is obtained as a consequence of a
formula for the third local cohomology module of the extended Rees algebras of
the $\mathbb Z^3$-graded filtration $\{\overline{I^rJ^sK^t}\}$ with support in
the ideal $(x_1t_1,x_2t_2,x_3t_3)$ where $(x_1,x_2,x_3)$ is a good joint
reduction of $\{\overline{I^rJ^sK^t}\}.$
