We present the projection operator method in combination with the
Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of
Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key
formulas of the method are couplings of the tensor and projection operators and
also a tensor form for the projection operator of U_q(su(3)). We obtain a very
compact general analytical formula for the U_q(su(3)) CGCs in terms of the
U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei),
(2001