Let \(L/\mathbb Q\) be an abelian extension with Galois group \(G\). The author completes the proof of the equivariant Tamagawa number conjecture for the Tate motive \(h^0(\text{Spec}(L))(j)\) with coefficients in \(\mathbb Z[G]\) for any integer \(j\) by providing a refined (i.e., equivariant) cyclotomic main conjecture at the prime \(2\). Note that this main conjecture at \(2\) was already stated as Theorem 5.2 in the author's survey article [Contemp. Math. 358, 79--125 (2004; Zbl 1070.11025)], but (as pointed out by the author) the proof given there, arguing separately for each height one prime ideal \(\mathfrak{q}\) of the cyclotomic Iwasawa algebra \(\Lambda = \mathbb Z_2[[\text{Gal}(\mathbb Q(\zeta_{2^{\infty}m}) / \mathbb Q)]]\) with \(2 \nmid m \in \mathbb Z\), is incomplete if \(2 \in \mathfrak q\). Here, the author uses techniques of his joint work with \textit{D.~Burns} [Doc. Math., J. DMV Extra Vol., 133--163 (2006; Zbl 1156.11042)] to verify the Cyclotomic Main Conjecture at \(2\). This conjecture states that a certain element \(\mathcal L\) obtained by \(2\)-adically interpolating the leading coefficients of Dirichlet \(L\)-functions at \(s=0\) is a \(\Lambda\)-basis of \(\mathrm{Det}_{\Lambda} \Delta^{\infty}\), where \(\Delta^{\infty}\) is a canonical perfect complex of \(\Lambda\)-modules constructed via etale cohomology. Note that a similar result for primes \(p \not=2\) was proven by \textit{D.~Burns} and \textit{C.~Greither} [Invent. Math. 153, No. 2, 303--359 (2003; Zbl 1142.11076)] building on a theorem of \textit{B.~Mazur} and \textit{A.~Wiles} [Invent. Math. 76, 179--330 (1984; Zbl 0545.12005)].