sorry to chime in that late, but: am I right that the problem is that we get the rotation matrix cos a -sin a sin a cos a inexact? and if so, how the inexactness is present? one of the diagonals is exactly +/-1 while the other is not exactly 0? in that case I'd suggest (would have suggested) to perform a paranoid normalization of the (cos a, sin a) vector, which e.g. normalizes (1, 1e-9) into (1, 0).
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