In PolarPlot, how to automatically fit the PolarTicks and show the radius ticks?

Question

PolarPlot[3 + 2 Cos[4*theta], {theta, 0, 2 Pi},
PolarAxes -> Automatic,
Axes -> False,
Frame -> False,
PolarTicks -> {Table[n*Pi/4, {n, 1, 8}], {1, 3, 5}}
]

gives

It does not give me the ticks for the radius, and does not look like the Ticks have all been fit too.

If I use

PolarPlot[3 + 2 Cos[4*theta], {theta, 0, 2 Pi},
    PolarAxes -> Automatic,
    PolarGridLines -> {Table[n*2 Pi/8, {n, 1, 8}], 
    Table[n, {n, 1, 5, 2}]},
    GridLinesStyle -> Directive[Gray, Dashed],
    PlotRange -> 8,
    Axes -> False,
    Frame -> False,
    PolarTicks -> {Table[n*Pi/4, {n, 1, 8}], {1, 3, 5}}
]

gives

Does I always to have change PlotRange -> XXX to fit it? Why aren't I getting the 1,2,3 ticks for the radius?

Answer 1

Set PlotRangeClipping -> False, PlotRangePadding -> 1.1, PolarAxes ->{True, True}.

But I still don't how to add another ticks.

PolarPlot[3 + 2 Cos[4*theta], {theta, 0, 2 Pi}, 
 PolarGridLines -> {Table[{n*2 Pi/8, Red}, {n, 1, 8}], {{1, Blue}, {3,
      Green}, {5, Cyan}}}, GridLinesStyle -> Directive[Gray, Dashed], 
 PlotRange -> 8, Axes -> False, Frame -> False, 
 PolarTicks -> {Table[n*Pi/4, {n, 1, 8}], {1, 3, 5}}, 
 PlotRangeClipping -> False, PlotRangePadding -> 1.1, 
 PolarAxes -> {True, True}]

Answer 2

To include minor ticks

PolarPlot[3 + 2 Cos[4*theta],
 {theta, 0, 2 Pi},
 PolarGridLines -> {
   Table[{n*2 Pi/8, Red}, {n, 1, 8}],
   {{1, Blue}, {3, Green}, {5, Cyan}}},
 GridLinesStyle ->
  Directive[AbsoluteThickness[.75], Dashed],
 PlotRange -> 8,
 PolarTicks -> {
   Join[Table[{n*Pi/4, n*Pi/4}, {n, 0, 7}],
    Table[{n*Pi/12, ""}, {n, 1, 24}]],
   Join[{#, #} & /@ {1, 3, 5, 7}, {#, ""} & /@ Range[1, 8, 1/2]]},
 PlotRangeClipping -> False,
 PlotRangePadding -> 1.1,
 PolarAxes -> {True, True},
 ImagePadding -> {{20, 20}, {30, 30}}]