  Monte Carlo simulations using the newly proposed Wang-Landau algorithm
together with the broad histogram relation are performed to study the
antiferromagnetic six-state clock model on the triangular lattice, which is
fully frustrated. We confirm the existence of the magnetic ordering belonging
to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral
ordering which occurs at slightly higher temperature. We also observe the lower
temperature phase transition of KT type due to the discrete symmetry of the
clock model. By using finite-size scaling analysis, the higher KT temperature
$T_2$ and the chiral critical temperature $T_c$ are respectively estimated as
$T_2=0.5154(8)$ and $T_c=0.5194(4)$. The results are in favor of the double
transition scenario. The lower KT temperature is estimated as $T_1=0.496(2)$.
Two decay exponents of KT transitions corresponding to higher and lower
temperatures are respectively estimated as $\eta_2=0.25(1)$ and
$\eta_1=0.13(1)$, which suggests that the exponents associated with the KT
transitions are universal even for the frustrated model.
