Mean Return Time and the Stationary Distribution

A Markov chain on $\{1, 2, 3\}$ has transition matrix $$P = \begin{pmatrix} 0 & \tfrac{1}{2} & \tfrac{1}{2} \\ \tfrac{1}{4} & \tfrac{1}{2} & \tfrac{1}{4} \\ \tfrac{1}{3} & \tfrac{1}{3} & \tfrac{1}{3} \end{pmatrix}.$$

(a) Find the stationary distribution $\pi$.

(b) Using the relationship between the stationary distribution and mean return times, compute the expected number of steps to return to state $1$ starting from state $1$.