Cabibbo Angle and Self-Consistency Condition

A solution of the $c$-number self-consistency condition $a_i-d_{\mathrm{ijk}}{a}_j{a}_k=h_i$ is obtained, where $a_i$ represents the matrix elements of unitary octet vector charge and $h_i$ is a driving term. With a reasonable choice of a driving term, we obtain $sin\theta =0.22-0.14\mathrm{}$ for the Cabibbo angle $\theta$. The choice of $h_i$ that leads to $tan\theta =\frac{m_n}{m_{\Lambda }}$ (where $m_n$ and $m_{\Lambda }$ are the quark masses) is also pointed out.