The definition of negative sequence as computed vectorially is something like
I- = Ia + alpha Ib + alpha^2 Ic where alpha is exp(j*120degrees). Or you may have to switch the coefficients of Ib and Ic. Please look it up and double check me.
So if you start with Ia, Ib, Ic, and want to compute directly from the definition, you need to figure out ways to come up with 120 degree phase shifts. One way is a 60 degree phase shift combined with reversal (180-60-120).
I'm suspect there are a variety of other ways to tackle it than to apply the definition directly.