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custom label/display for a Manipulate slider?


So I'm trying to make a somewhat simple unit-circle, and have a slider control within Manipulate that lets the user change theta at the usual steps from 0 to 2Pi. When I use Appearance ->"Labeled" for the slider, it shows the value of theta but in decimals - is there any way to make it show the exact values? I'm assuming I'd have to type out that list somewhere in the code, but as I move the slider, I want it to display Pi/6, 4Pi/3, etc. Is there an easy way to do this?


    {Gray, Circle[{0, 0}, 1]},
    {Darker[Green, 0.2], Thick, Circle[{0, 0}, 1, {0, theta}]},
    {Darker[Gray], Line[{{0, 0}, {Cos[theta], Sin[theta]}}]},
    {Darker[Blue, 0.1], Thickness[0.006],
     Line[{{Cos[theta], 0}, {Cos[theta], Sin[theta]}}]},
    {Darker[Red, 0.1], Thickness[0.006],
     Line[{{0, 0}, {Cos[theta], 0}}]},
  PlotRange -> 2, ImageSize -> 300, Axes -> True,
  Ticks -> {{-1, 1}, {-1, 1}}
 {theta, {0, \[Pi]/6, \[Pi]/4, \[Pi]/3, \[Pi]/2, 2 \[Pi]/3, 3 \[Pi]/4,
    5 \[Pi]/6, \[Pi], 7 \[Pi]/6, 5 \[Pi]/4, 4 \[Pi]/3, 3 \[Pi]/2,
   5 \[Pi]/3, 7 \[Pi]/4, 11 \[Pi]/6, 2 \[Pi]}, ControlType -> Slider,
  Appearance -> "Labeled"

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