A doubly stochastic two-state chain has the uniform stationary law

Let $\{X_n\}$ be a doubly stochastic Markov chain on $\{0,1\}$ with $P[X_{n+1}=1\mid X_n=1]=p_1$ and $P[X_{n+1}=1\mid X_n=0]=p_0$, and $\pi_1=P(X=1)$. What is the value of $\pi_1$?