Radon Nikodym derivative of the irrational rotation of the circle $S^1$

Question

Let $S^1$ be the unit circle and let $\tau$ be the irrational rotation of the circle defined by $\tau(e^{2\pi ix})=e^{2\pi i(x+\alpha)}$. Let $du=\frac{1}{2\pi}d\lambda$ where $\lambda$ is the Lebesgue measure on $S^1$. I am unable to find the Radon Nikodym derivative of $\frac{du \circ \tau}{du}$. I know the Haar measure is invariant under rotation.