smc

This is equivalent to $\frac{(a-1{)}^6}{a^6}.$ Its expansion has 7 terms, whose coefficients are the same as those of $(a-1{)}^6$. By the Binomial Theorem, the sum of the last three coefficients is $\left(\genfrac{}{}{0ex}{}{6}{2}\right)-\left(\genfrac{}{}{0ex}{}{6}{1}\right)+\left(\genfrac{}{}{0ex}{}{6}{0}\right)=15-6+1=\boxed{10}$.