  This paper is a next step in the project of systematic description of colored
knot polynomials started in arXiv:1506.00339. In this paper, we managed to
explicitly find the $\textit{inclusive}$ Racah matrices, i.e. the whole set of
mixing matrices in channels $R^{\otimes 3}\longrightarrow Q$ with all possible
$Q$, for $R=[3,3]$. The case $R=[3,3]$ is a multiplicity free case as well as
$R=[2,2]$ obtained in arXiv:1605.03098. The calculation is made possible by the
use of highest weight method with the help of Gelfand-Tseitlin tables. The
result allows one to evaluate and investigate $[3,3]$-colored polynomials for
arbitrary 3-strand knots, and this confirms many previous conjectures on
various factorizations, universality, and differential expansions. With the
help of a method developed in arXiv:1605.04881 we manage to calculate {\it
exclusive} Racah matrices $S$ and $\bar S$ in $R=[3,3]$. Our results confirm a
calculation of these matrices in arXiv:1606.06015, which was based on the
conjecture of explicit form of differential expansion for twist knots. Explicit
answers for Racah matrices and $[3,3]$-colored polynomials for 3-strand knots
up to 10 crossings are available at http://knotebook.org.
