Solution
= Solution
Completing the square gives
$$
\boxed{\theta\mid y\sim N(\widetilde\theta,\sigma_\theta^2)},
\qquad
\widetilde\theta=\frac{\tau^2}{\sigma^2+\tau^2}y,
\qquad
\sigma_\theta^2=\frac{\sigma^2\tau^2}{\sigma^2+\tau^2}.
$$
= Solution
Completing the square gives
$$
\boxed{\theta\mid y\sim N(\widetilde\theta,\sigma_\theta^2)},
\qquad
\widetilde\theta=\frac{\tau^2}{\sigma^2+\tau^2}y,
\qquad
\sigma_\theta^2=\frac{\sigma^2\tau^2}{\sigma^2+\tau^2}.
$$