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PolarPlot[ Exp[Cos[\[Theta]]] - 2 Cos[4 \[Theta]] +
  Sin[\[Theta]/12]^5, {\[Theta], 0, 20 Pi}, PolarAxes -> Automatic,
PlotStyle -> Red,  PolarGridLines -> {{0, Pi/4, Pi/2, 3 Pi/4, Pi, 5 Pi/4, 3 Pi/2}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}, PolarTicks -> {"Degrees", Automatic}]
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