For this particular plot you can use Graphics instead of PolarPlot:

Graphics[{{Yellow, 
   Polygon[Join[{AngleVector[{2, Pi/3}], AngleVector[{1, Pi/3}], 
      AngleVector[{1, Pi/3}]}, 
     Join[{AngleVector[{2, Pi/3}], AngleVector[{1, Pi/3}], 
       AngleVector[{1, Pi/3}]}, 
      Table[AngleVector[{2, theta}], {theta, Pi/6, Pi/3, Pi/30}]]]]}, 
  Circle[{0, 0}, 1, {Pi/6, Pi/3}], Circle[{0, 0}, 2, {Pi/6, Pi/3}],
  Line[{{0, 0}, AngleVector[{2, Pi/6}]}], 
  Line[{{0, 0}, AngleVector[{2, Pi/3}]}], Dashed, 
  Line[{AngleVector[Pi/3], AngleVector[{2, Pi/6}]}]}, Axes -> True]

However, you can alternatively take the Polygon above and paste it into a Prolog to PolarPlot.