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}]


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?

Animate[ParametricPlot[{Cos[t], Sin[t]}, {t, a, a + 2 Pi - Pi/8},