  Seven different triple sum formulas for $9j$ coefficients of the quantum
algebra $u_q(2)$ are derived, using for these purposes the usual expansion of
$q$-$9j$ coefficients in terms of $q$-$6j$ coefficients and recent summation
formula of twisted $q$-factorial series (resembling the very well-poised basic
hypergeometric $_5\phi_4$ series) as a $q$-generalization of Dougall's
summation formula of the very well-poised hypergeometric $_4F_3(-1)$ series.
This way for $q=1$ the new proof of the known triple sum formula is proposed,
as well as six new triple sum formulas for $9j$ coefficients of the SU(2)
group, in the angular momentum theory. The mutual rearrangement possibilities
of the derived triple sum formulas by means of the Chu--Vandermonde summation
formulas are considered and applied to derive several versions of double sum
formulas for the stretched $q$-$9j$ coefficients, which give new rearrangement
and summation formulas of special Kamp\'e de F\'eriet functions and their
$q$-generalizations. Several fourfold sum formulas [with each sum of the
$_5F_4(1)$ or $_5\phi_4$ type] for the $12j$ coefficients of the second kind
(without braiding) of the SU(2) and $u_q(2)$ are proposed, as well as
expressions with five sums [of the $_4F_3(1)$ and $_3F_2(1)$ or $_4\phi_3$ and
$_3\phi_2$ type] for the $12j$ coefficients of the first kind (with braiding)
instead of the usual expansion in terms of $q$-$6j$ coefficients. Stretched and
doubly stretched $q$-$12j$ coefficients [as triple, double or single sums,
related to composed or separate hypergeometric $_4F_3(1)$ and $_5F_4(1)$ or
$_4\phi_3$ and $_5\phi_4$ series, respectively] are considered.
