  We make phenomenological predictions for particle spectra and elliptic flow
in heavy-ion collisions using 3+1d anisotropic hydrodynamics (aHydro) including
the effects of both shear and bulk viscosities. The dynamical equations
necessary are derived by taking moments of the Boltzmann equation allowing for
three distinct (diagonal) momentum-space anisotropy parameters. The formulation
is based on relaxation-time approximation for the collisional kernel and a
lattice-QCD-based equation of state. Evolving the system to late times, we
calculate particle production using THERMINATOR 2, modified to account for an
ellipsoidal distribution function. We obtain particle spectra for different
particle species such as pions, kaons, and protons, and elliptic flow $v_2$ as
a function of centrality, transverse momentum, and rapidity. In our model, we
have four free parameters, i.e. freeze-out temperature, initial central energy
density, initial momentum-space anisotropies, and shear viscosity to entropy
density ratio. Using a multidimensional fit to LHC experimental data, we make a
preliminary extraction of these parameters. We find reasonable agreement
between 3+1d aHydro and available experimental data for $\eta/s\sim 0.23$.
