The sharp bound of the third Hankel determinant for functions of bounded turning

We find the sharp bound for the third Hankel determinant $$\begin{aligned} H_{3,1}(f):= \left| {\begin{array}{*{20}c} {a_{1} } & {a_{2} } & {a_{3} } \\ {a_{2} } & {a_{3} } & {a_{4} } \\ {a_{3} } & {a_{4} } & {a_{5} } \\ \end{array} } \right| \end{aligned}$$ for analytic functions f with $$a_n:=f^{(n)}(0)/n!,\ n\in \mathbb N,\ a_1:=1,$$ such that $$\begin{aligned} {{\,\mathrm{Re}\,}}f'(z)>0,\quad z\in \mathbb D:=\{z \in \mathbb C: |z|<1\}. \end{aligned}$$