Quantum [Formula: see text]-matrices are the building blocks for the colored HOMFLY polynomials. In the case of three-strand braids with an identical finite-dimensional irreducible representation [Formula: see text] of [Formula: see text] associated with each strand, one needs two matrices: [Formula: see text] and [Formula: see text]. They are related by the Racah matrices [Formula: see text]. Since we can always choose the basis so that [Formula: see text] is diagonal, the problem is reduced to evaluation of [Formula: see text]-matrices. This paper is one more step on the road to simplification of such calculations. We found out and proved for some cases that [Formula: see text]-matrices could be transformed into a block-diagonal ones by the rotation in the sectors of coinciding eigenvalues. The essential condition is that there is a pair of accidentally coinciding eigenvalues among eigenvalues of [Formula: see text] matrix. In this case in order to get a block-diagonal matrix, one should rotate the [Formula: see text] defined by the Racah matrix in the accidental sector by the angle exactly [Formula: see text].