On an estimate in the class of typically real functions

Let $T(c_2,c_3)$ be the class of functions $f(z)=z+\sum^\infty_{n=2}c_nz^n$ regular and typically real in the disk $|z|<1$ with fixed values of the coefficients $c_2$ and $c_3$. The boundary functions of the region of values of $f(z_0)$ $(0<|z_0|<1)$ and sharp estimates for $f(r)$, $0<r<1$, in the class $T(c_2,c_3)$ are determined.