The calculation is as following. If \(\rho = 1\), then \(\theta_{11} =
pq\), \(\theta_{01} = (1-p)q\), \(\theta_{10} = p(1-q)\), and
\(\theta_{00} = (1-p)(1-q)\). Otherwise, \( \theta_{11} = -(\sqrt{A+B}\),
\(\theta_{01} = q-\theta_{11}\), \(\theta_{10} = p-\theta_{11}\), and
\(\theta_{00} = \theta_{01}\theta_{10}\rho/\theta_{11}\), where
\(A=(p+q-p \rho-q\rho-1)^2-4(\rho-1)pq\rho)\) and
\(B=(p+q-p\rho-q\rho-1))/2/(\rho-1)\).