Einfärben von der Fläche zwischen 3 Ellipsen

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}

\usetikzlibrary{intersections}
\begin{document}
\pgfdeclarelayer{pre main}
\begin{tikzpicture}
\pgfsetlayers{pre main,main}

\pgfmathsetmacro{\radiusA}{1*90 / 120)}%
\draw [name path = Kreis1] (-4,0) arc (180:360:4 cm and \radiusA cm);
%Waagerecht

\pgfmathsetmacro{\radiusB}{4*cos(270-10)}%
\draw [name path = Kreis2] (0,4) arc (90:270:\radiusB cm and 4 cm);

\begin{scope}[rotate = -30]
\draw[name path = Kreis3] (0:4) arc (0:180:4 cm and 2.5 cm);
\end{scope}

% first: intersect 1 and 2, remember as temp path
\path [
    %->,red,orange, % <-- for experiments
    intersection segments={
        of=Kreis1 and Kreis2,
        sequence={L2[reverse] -- R1[reverse]},
    },
    name path=lowerleft,
];

\pgfonlayer{pre main}
% now: intersect intermediate result with Kreis3
\fill [
    %->,thick,
    orange,
    intersection segments={
        of=lowerleft and Kreis3,
        sequence={L2 -- R2[reverse]},
    },
];
\endpgfonlayer
\end{tikzpicture}
\end{document}