  Let $\Omega \subset \mathbb R^3$ be a broken sheared waveguide, i.e., it is
built by translating a cross-section in a constant direction along a broken
line in $\mathbb R^3$. We prove that the discrete spectrum of the Dirichlet
Laplacian operator in $\Omega$ is non-empty and finite. Furthermore, we show a
particular geometry for $\Omega$ which implies that the total multiplicity of
the discrete spectrum is equals 1.
