  While the angular-momentum projection is a common tool for theoretical
nuclear structure studies, a large amount of computations are required
particularly for triaxially deformed states.
  In the present work, we clarify the conditions of the exactness of
quadratures in the projection method. For efficient computation, the Lebedev
quadrature and spherical $t$-design are introduced to the angular-momentum
projection.
  The accuracy of the quadratures is discussed in comparison with the
conventional Gauss-Legendre and trapezoidal quadratures. We found that the
Lebedev quadrature is the most efficient among them and the necessary number of
sampling points for the quadrature, which is often proportional to the
computation time, is reduced by a factor 3/2 in comparison with the
conventional method.
