  We have studied the $N^*(1875) (3/2^-)$ resonance with a multichannel unitary
scheme, considering the $\Delta \pi$ and $\Sigma^* K$, with their interaction
extracted from chiral Lagrangians, and then have added two more channels, the
$N^*(1535) \pi$ and $N \sigma$, which proceed via triangle diagrams involving
the $\Sigma^* K$ and $\Delta \pi$ respectively in the intermediate states. The
triangle diagram in the $N^*(1535) \pi$ case develops a singularity at the same
energy as the resonance mass. We determine the couplings of the resonance to
the different channels and the partial decay widths. We find a very large decay
width to $\Sigma^* K$, and also see that, due to interference with other terms,
the $N \sigma$ channel has an important role in the $\pi \pi$ mass
distributions at low invariant masses, leading to an apparently large $N
\sigma$ decay width. A discussion is done, justifying the convenience of an
experimental reanalysis of this resonance to the light of the findings of the
paper, using multichannel unitary schemes.
