TikZ: using decorations.markings to decorate a clipped path

I clipped a circle along the line atan(2/3). Where the circle is clipped I would like to put an arrow. I thought it would be as simple as (atan(2/3) + 180)/360 to get its percentage location along the path. Unfortunately, it wasn't. I ended up subtracting 32.5 degrees due to trial and error. I would like to make a more exact placement though.

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}

\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\angle}{atan(2/3)};
\pgfmathsetmacro{\ppi}{\angle + 180};
\pgfmathsetmacro{\percent}{(\ppi - 32.5)/360};

\begin{scope}[rotate = \angle, decoration = {
markings,
mark = at position \percent with {\arrow{stealth}}
}]
\clip (0, .4) rectangle (-.45, 0);

\draw[postaction = decorate] (cylinder) circle[radius = .395cm];
\end{scope}
\end{tikzpicture}
\end{document}


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Let us analyse. Without \clip,without rotation and the drawn rectangle this is your circle:

This shows that the \percent value should be 50. With

\pgfmathsetmacro{\ppi}{\angle + 180};
\pgfmathsetmacro{\percent}{(\ppi)/360};


You are certainly not giving 50% but more than that. To be exact, you are giving atan(2/3) more to \ppi. If we make \ppi = 180, then \percent will be 50.

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}

\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\angle}{atan(2/3)};
\pgfmathsetmacro{\ppi}{180};
\pgfmathsetmacro{\percent}{(\ppi)/360};

\begin{scope}[rotate = 0, decoration = {%     % change rotate to \angle
markings,
mark = at position \percent with {\arrow{stealth}}
}]
%\clip (0, .4) rectangle (-.45, 0);
\draw (0, .4) rectangle (-.45, 0);

\draw[postaction = decorate] (0,0) circle[radius = .395cm];
\end{scope}
\end{tikzpicture}
\end{document}


Now you can rotate and clip to get:

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}

\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro{\angle}{atan(2/3)};
\pgfmathsetmacro{\ppi}{180};
\pgfmathsetmacro{\percent}{(\ppi)/360};

\begin{scope}[rotate = \angle, decoration = {
markings,
mark = at position \percent with {\arrow{stealth}}
}]
\clip (0, .4) rectangle (-.45, 0);
%\draw (0, .4) rectangle (-.45, 0);

\draw[postaction = decorate] (0,0) circle[radius = .395cm];
\end{scope}
\end{tikzpicture}
\end{document}


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