shading region bounded by several curves

Question

I have the following code:

\documentclass{book}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture} 
\draw [color=red,fill=red,fill opacity=1.0] (-0.67,1.06) circle (2.41cm);
\draw [color=white,fill=white,fill opacity=1.0] (-0.66,1.71) circle (1.92cm);
\draw [shift={(-0.05,2.21)},color=red]  plot[domain=2.01:4.03,variable=\t]({1.*1.40*cos(\t r)+0.*1.40*sin(\t r)},{0.*1.40*cos(\t r)+1.*1.40*sin(\t r)});
\draw [shift={(-1.60,0.27)},color=red]  plot[domain=-0.48:0.92,variable=\t]({1.*1.08*cos(\t r)+0.*1.08*sin(\t r)},{0.*1.08*cos(\t r)+1.*1.08*sin(\t r)});
\draw [shift={(-1.26,1.06)},color=red]  plot[domain=-1.12:0.68,variable=\t]({1.*1.43*cos(\t r)+0.*1.43*sin(\t r)},{0.*1.43*cos(\t r)+1.*1.43*sin(\t r)});
\draw [shift={(0.42,3.0)},color=red] plot[domain=2.72:4.215,variable=\t]({1.*1.18*cos(\t r)+0.*1.18*sin(\t r)},{0.*1.18*cos(\t r)+1.*1.18*sin(\t r)});  
\end{tikzpicture}
\end{document}

And I want to color red the thing in center. I've read this and do:

\documentclass{book}
\usepackage{tikz}

\tikzset{
saveuse path/.code 2 args={
    \pgfkeysalso{#1/.style={insert path={#2}}}%
    \global\expandafter\let\csname pgfk@\pgfkeyscurrentpath/.@cmd\expandafter\endcsname
    % not optimal as it is now global through out the document
    \csname pgfk@\pgfkeyscurrentpath/.@cmd\endcsname
    \pgfkeysalso{#1}},
/pgf/math set seed/.code=\pgfmathsetseed{#1}}

\begin{document}
        \begin{tikzpicture}
        \begin{scope}       
        \clip [saveuse path={plot path}{plot[smooth, samples=100, domain=2.01:4.03,variable=\t]({1.*1.40*cos(\t r)+0.*1.40*sin(\t r)},{0.*1.40*cos(\t r)+1.*1.40*sin(\t r)}) }]-- (0,0) --(0,2) -- cycle;

        \clip [saveuse path={plot path}{plot[smooth, samples=100, domain=-0.48:0.92,variable=\t]({1.*1.08*cos(\t r)+0.*1.08*sin(\t r)},{0.*1.08*cos(\t r)+1.*1.08*sin(\t r)}) }]-- (0,0) --(0,-1.5) -- cycle;

        \clip [saveuse path={plot path}{plot[smooth, samples=100, domain=-1.12:0.68,variable=\t]({1.*1.43*cos(\t r)+0.*1.43*sin(\t r)},{0.*1.43*cos(\t r)+1.*1.43*sin(\t r)}) }]-- (0,0) --(0,-1.5) -- cycle;

        \clip [saveuse path={plot path}{plot[smooth, samples=100, domain=2.72:4.215,variable=\t]({1.*1.18*cos(\t r)+0.*1.18*sin(\t r)},{0.*1.18*cos(\t r)+1.*1.18*sin(\t r)}) }]-- (0,0) --(0,2) -- cycle;  

        \end{scope}
        \draw [plot path];
        \end{tikzpicture}           

\end{document}

But it don't work. How can I solve this? *Please not xelatex