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I have the following animated parametric curve where the gap looks like it's rotating in the counterclockwise direction.

Animate[ParametricPlot[{Cos[t], Sin[t]}, {t, a, a + 2 Pi - Pi/8}, 
Axes -> False, PlotStyle -> {Thick, Purple}], {a, 0, 10}]

enter image description here

I'd like to add an arrow to the endpoint so that is appears to point in the direction of rotation. Is there a simple way to do this?

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Animate[ParametricPlot[{Cos[t], Sin[t]}, {t, a, a + 2 Pi - Pi/8}, 
Axes -> False, PlotStyle -> {Thick, Purple}] /. Line -> Arrow, {a,0,10}]

enter image description here

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