  This article discusses some topological properties of the dynamical plane
($z$-plane) of the holomorphic family of meromorphic maps $\lambda + \tan z^2$
for $ \lambda \in \mathbb C$. In the dynamical plane, we prove that there is no
Herman ring, and the Julia set is a Cantor set for the maps when the parameter
is in the unbounded hyperbolic component contained in the four quadrants in the
complex plane. Julia set is connected for the maps when the parameters are in
other hyperbolic components of the parameter plane.
