Tikz: even odd rule with intersecting shapes

Question

I do not know how to use the even odd rule to fill intersecting shapes. This is the desired outcome:

And this is my code. I'd appreciate an explanation of how to apply the even odd rule, when to use clip and when to use scope, which I have seen used in simpler examples of this kind. Thanks!
documentclass[border=3pt,tikz]{standalone}

% define the angle theta = pi/7
deftheta{25.71}
% define the circle of radius 1
defshapeA{(0,0) circle (1cm)}
% define the annulus of radii 1 and 2
defshapeB{(0,0) circle (1cm) (0,0) circle (2cm)}
% define the annulus of radii 2 and 3
defshapeC{(0,0) circle (2cm) (0,0) circle (3cm)}
% define the intersecting lines
% attempted to group them for even-odd rule
%defshapeD{(180+theta:3.5cm) -- (0,0) -- (theta:3.5cm)}
%defshapeE{(-theta:3.5cm) -- (0,0) -- (180-theta:3.5cm)}
defshapeD{(-theta:3.5cm) -- (0,0) -- (theta:3.5cm)}
defshapeE{(180+theta:3.5cm) -- (0,0) -- (180-theta:3.5cm)}

begin{document}

begin{tikzpicture}[thick]
  fill[fill=lightgray, even odd rule]  shapeE shapeB;
  fill[fill=lightgray, even odd rule]  shapeD shapeA;
  draw shapeA shapeB shapeC shapeD shapeE;
end{tikzpicture}

end{document}

SebGlav · Accepted Answer

You complicated too much.

documentclass[border=3pt,tikz]{standalone}

% define the angle theta = pi/7
deftheta{25.71}
defshapeA{(0,0) circle (1cm)}
defshapeB{(0,0) circle (2cm)}
defshapeC{(0,0) circle (3cm)}

defshapeD{(-theta:3.5cm) -- (0,0) -- (theta:3.5cm)}
defshapeE{(180+theta:3.5cm) -- (0,0) -- (180-theta:3.5cm)}

begin{document}

begin{tikzpicture}[thick]
    begin{scope}
        clip shapeC;
        fill[fill=lightgray, even odd rule]  shapeE shapeB shapeD shapeA;
    end{scope}
  
  draw shapeA shapeB shapeC shapeD shapeE;
end{tikzpicture}

end{document}

Just declare all your shapes, in a simple way (here, for example, the circles needed to be declared as they are, not as annuli like you tried to). Then fill with even odd rule  all the shapes together.
As for the clip, here you don't want to fill outside the larger circle, so you scope the filling with a clip shapeC;, meaning that, inside your scope environment, nothing is drawn outside shapeC. And you finally draw your lines outside the scope environment to let them be drawn outside the larger circle.

mickep · Answer

Since there is already a nice and accepted answer, I feel free to add a solution using nofill and eofill from MetaPost/MetaFun. Mostly for fun, but I hope someone could have a use for it! The file is compiled with context.
startMPpage[offset=3bp]
u:=1cm;

path circle[],line[];

for i=0 upto 2:
circle[i] = fullcircle scaled (2(i+1)*u);
endfor

line0 = ((-1,0)--(1,0)) rotated 360/28 scaled 4u;
line1 = line0 rotated (180-360/14);

nofill circle1;
nofill line0 -- line1 -- cycle;
eofill circle0 withcolor lightgray;
clip currentpicture to circle2;

for i=circle0,circle1,circle2,line0,line1:
draw i;
endfor
stopMPpage

The result shows as follows:

Tikz: even odd rule with intersecting shapes

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