  A sensitivity study of the unbinned angular analysis of the $B\to
D^*(D\pi)\ell \nu_\ell$ decay is presented. In the analysis, it is shown that
the Wilson coefficient of the right-handed vector current, $C_{V_R}$, can be
measured to precision of 2-4$\%$ using either the full set of normalised
angular observables or the forward-backward asymmetry $A_{FB}$ of the charged
lepton in 10 $w$ bins. Such angular measurements are independent of the
$V_{cb}$ puzzle.
