= Solution
{c}
The <Clifford algebra> of the <gamma matrices> gives $\gamma^\nu\gamma^\mu=2g^{\nu\mu}-\gamma^\mu\gamma^\nu$ and $\gamma^\nu\gamma_\nu=D\mathbf1$. Therefore
$$
\gamma^\nu\gamma^\mu\gamma_\nu=2g^{\nu\mu}\gamma_\nu-\gamma^\mu\gamma^\nu\gamma_\nu=2\gamma^\mu-D\gamma^\mu,
\qquad\boxed{\gamma^\nu\gamma^\mu\gamma_\nu=(2-D)\gamma^\mu.}
$$
The contraction $g^\nu{}_{\nu}=D$ must be retained until the <dimensional regularization> calculation is complete; replacing it prematurely by four can change finite terms multiplying a <ultraviolet pole>.
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