  In this short note we will provide a new and shorter proof of the following
exotic shuffle relation of multiple zeta values:
  $$\zeta(\{2\}^m \sha\{3,1\}^n)={2n+m\choose m}
  \frac{\pi^{4n+2m}}{(2n+1)\cdot (4n+2m+1)!}.$$ This was proved by Zagier when
n=0, by Broadhurst when $m=0$, and by Borwein, Bradley, and Broadhurst when
m=1. In general this was proved by Bowman and Bradley in \emph{The algebra and
combinatorics of shuffles and multiple zeta values}, J. of Combinatorial
Theory, Series A, Vol. \textbf{97} (1)(2002), 43--63. Our idea in the general
case is to use the method of Borwein et al. to reduce the above general
relation to some families of combinatorial identities which can be verified by
WZ-method.
