  In this proceedings, we lay the foundation for computing the contribution of
quark chromo-electric dipole moment (qCEDM) operator to the nucleon electric
dipole moment. By applying the gradient flow technique, we can parameterize the
renormalization and operator mixing issues associated with the qCEDM operator
on the lattice. As the nucleon mixing angle $\alpha_N$ is a key component for
determining the neutron and proton electric dipole moments induced by the qCEDM
operator, we present the formalism and preliminary results for $\alpha_N$ with
respect to the gradient flow time $t_f$. The results are computed on $N_f=2+1$
Wilson-clover lattices provided by PACS-CS. The 3 ensembles have lattice
spacing values of $a=\lbrace 0.1095,\,0.0936,\,0.0684\rbrace $fm, whilst
keeping a similar $m_{\pi}\approx701$MeV, and a fixed box size of
$L\approx1.9$fm.
