Arrows with curved line [closed]

Question

I Need to reproduce a figure somewhat like the one here: Drawing Angles

The problem is that I get a figure wich differ from the original one: the arrow at the end of the spiral get vertical direction.

What's wrong here.

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            axis lines=middle,
            axis equal image,
            enlargelimits,
            xtick=\empty, ytick=\empty,
            data cs=polar,
            samples=100
        ]
            \addplot [thick, black, smooth, domain=0:360] {1};
            \addplot [thick, red, -latex, smooth, domain=0:405] {0.3+x/2000} node [pos=0.9, anchor=south west] {$405^\circ$};
            \addplot [thick, black] coordinates {(0,0) (405,1)};
        \end{axis}
    \end{tikzpicture}
\end{document}