  We develop a systematic approach to deriving addition theorems for, and some
other bilocal sums of, spin spherical harmonics. In this first part we
establish some necessary technical results. We discuss the factorization of
orbital and spin degrees of freedom in certain products of Clebsch-Gordan
coefficients, and obtain general explicit results for the matrix elements in
configuration space of tensor products of arbitrary rank of the position and
angular-momentum operators. These results are the basis of the addition
theorems for spin spherical harmonics obtained in part II.
