  We study the quantum phase transition between the $Z_2$ spin liquid and
valence bond solid (VBS) orders on a triangular lattice. With a fully isotropic
triangular lattice, the transition from a columnar or resonating-plaquette VBS
order can be either first order or there could be two transitions with an
intermediate phase. If the transition splits into two, then the $Z_2$ spin
liquid will first experience a first order $q=3$ Potts transition to a new
nematic $Z_2$ spin liquid that breaks the $2\pi/3$ lattice rotation symmetry
(but retain translation symmetry unlike the VBS states). The second transition
will then take this new nematic $Z_2$ spin liquid to a columnar or
resonating-plaquette VBS state through a second order $3d$ XY$^*$ transition.
On a distorted triangular lattice, the degeneracy between some of the different
columnar VBS orders is lifted, and the phase transition can reduce to a single
$3d$ XY$^*$ transition.
