Wie kann ich einen mit der tikz angle library erzeugten Winkel neigen?

\documentclass{standalone}
\usepackage{tikz,tikz-3dplot}

\renewcommand\tdplotdrawpolytopearc[4][]{%

    %determine vector lengths
    \pgfmathsetmacro{\ax}{\tdplotax - \tdplotvertexx}
    \pgfmathsetmacro{\ay}{\tdplotay - \tdplotvertexy}
    \pgfmathsetmacro{\az}{\tdplotaz - \tdplotvertexz}

    \pgfmathsetmacro{\bx}{\tdplotbx - \tdplotvertexx}
    \pgfmathsetmacro{\by}{\tdplotby - \tdplotvertexy}
    \pgfmathsetmacro{\bz}{\tdplotbz - \tdplotvertexz}

    %determine normal to vectors
    \tdplotcrossprod(\ax,\ay,\az)(\bx,\by,\bz)

    %DEBUG: show the cross product
    %\draw[->,blue] (\tdplotvertexx,\tdplotvertexy,\tdplotvertexz) 
        -- ++(\tdplotresx,\tdplotresy,\tdplotresz);

    %get angles for this vector
    \tdplotgetpolarcoords{\tdplotresx}{\tdplotresy}{\tdplotresz}

    \typeout{angles for cross product: phi: \tdplotresphi theta: \tdplotrestheta}

    %place the rotated coordinate system so that the z' axis points along this vector
    \tdplotsetrotatedcoords{\tdplotresphi}{\tdplotrestheta}{0}
    \coordinate (Vertex) at (\tdplotvertexx,\tdplotvertexy,\tdplotvertexz);
    \tdplotsetrotatedcoordsorigin{(Vertex)}

    %calculate the start angle of the arc
    \tdplottransformmainrot{\ax}{\ay}{\az}
    \tdplotgetpolarcoords{\tdplotresx}{\tdplotresy}{\tdplotresz}
    \pgfmathsetmacro{\tdplotstartphi}{\tdplotresphi}

    %calculate the end angle of the arc
    \tdplottransformmainrot{\bx}{\by}{\bz}
    \tdplotgetpolarcoords{\tdplotresx}{\tdplotresy}{\tdplotresz}

    %draw the arc
    \pgfmathparse{\tdplotstartphi < \tdplotresphi}
    \ifthenelse{\equal{\pgfmathresult}{1}}%
        {}%
        {
            \pgfmathsetmacro{\tdplotstartphi}{\tdplotstartphi - 360}
        }

    \draw[tdplot_rotated_coords,#1] (0,0,0) + (\tdplotstartphi:#2) arc (\tdplotstartphi:\tdplotresphi:#2);

    \fill[tdplot_rotated_coords,#1] (0,0,0) + (\tdplotstartphi:#2) arc (\tdplotstartphi:\tdplotresphi:#2) -- (0,0,0) -- (\tdplotstartphi:#2);

    \pgfmathsetmacro{\tdplotresphi}{(\tdplotresphi + \tdplotstartphi)/2}

    \draw[tdplot_rotated_coords] (0,0,0) + (\tdplotresphi:#2) node[#3]{#4};
}

\newcommand\tdplotsetmycoords{%
  \pgfmathsetmacro{\raarot}{-.5}%
  \pgfmathsetmacro{\rbarot}{-.5}%
  % 
  \pgfmathsetmacro{\rabrot}{1}%
  \pgfmathsetmacro{\rbbrot}{0}%
  % 
  \pgfmathsetmacro{\racrot}{0}%
  \pgfmathsetmacro{\rbcrot}{1}%
  % 
  \tikzset{tdplot_main_coords/.style={x={(\raarot cm,\rbarot cm)},y={(\rabrot cm, \rbbrot cm)},z={(\racrot cm, \rbcrot cm)}}}%
}

\begin{document}

\tdplotsetmycoords
\begin{tikzpicture}[scale=2,tdplot_main_coords]
  \tdplotdefinepoints(0,0,0)(1.5,0,0)(1.5,2.5,1.75)

  \coordinate (O) at (\tdplotvertexx,\tdplotvertexy,\tdplotvertexz);
  \coordinate (Ax) at (\tdplotbx,0,0);
  \coordinate (Ay) at (0,\tdplotby,0);
  \coordinate (Az) at (0,0,\tdplotbz);
  \coordinate (Axy) at (\tdplotbx,\tdplotby,0);
  \coordinate (Ayz) at (0,\tdplotby,\tdplotbz);
  \coordinate (Axz) at (\tdplotbx,0,\tdplotbz);
  \coordinate (A) at (\tdplotbx,\tdplotby,\tdplotbz);

  \draw[->] (0,0,0) -- (2,0,0) node[below left=-2pt] {$x$};
  \draw[->] (0,0,0) -- (0,3,0) node[right] {$y$};
  \draw[->] (0,0,0) -- (0,0,2) node[above] {$z$};
  \draw[thick] (Ax) -- (Axy) -- (Ay);
  \draw[thick] (Az) -- (Axz) -- (A) -- (Ayz) -- cycle;
  \draw[thick] (O) -- (Az);
  \draw[thick] (Ax) -- (Axz);
  \draw[thick] (Axy) -- (A);
  \draw[thick] (Ay) -- (Ayz);
  \draw[red,thick,->] (O) -- (Ax) node[pos=0.7,above] {a};
  \draw[red,thick,->] (O) -- (Ay);
  \draw[red,thick,->] (O) -- (Az);
  \draw[red,thick,->] (O) -- (A) node[above,pos=0.5] {d};

  \tdplotdrawpolytopearc[blue,thick,fill opacity=0.1]{1}{above left=-4pt,blue}{$\theta$}
\end{tikzpicture}
\end{document}