  Spectroscopy of discrete Landau levels (LLs) in bulk-insulating
three-dimensional topological insulators (3D TIs) in perpendicular magnetic
field characterizes the Dirac nature of their surface states. Despite a number
of studies demonstrating the quantum Hall effect (QHE) of topological surface
states, quantitative evaluation of the LL energies, which serve as fundamental
electronic quantities for study of the quantum states, is still limited. In
this work, we explore the density of states of LLs by measuring quantum
capacitance (CQ) in a truly bulk insulating 3D TI via a van der Waals
heterostructure configuration. By applying dual gate voltages, we access the
individual surface states' LLs and extract their chemical potentials to
quantify the LL spacings of each surface. We evaluate the LLs' energies at two
distinguished QH states, namely dissipationless ({\nu}= +/-1) and dissipative
({\nu}= 0) states in the 3D TI.
