A rotation theorem in the class of bounded univalent functions

Let $S_M$, $M>1$, be the class of functions $f(z)$ which are regular and univalent in the disk $|z|<1$ and satisfy the conditions $f(0)=0$, $f'(0)=1$, $|f(z)|<M$. In the present note we will obtain an exact estimate for the argument of the derivative of a function of the class $S_M$.