// Using 1.2 API
static class CoolDownPathAnimation
{
  public static DependencyProperty RotationProperty = DependencyProperty.RegisterAttached(
    "Rotation", typeof(float), typeof(CoolDownPathAnimation),
    new PropertyMetadata(0.0f, new PropertyChangedCallback(OnRotationChanged));

  public static float GetRotation(DependencyObject element)
  {
    return (float)element.GetValue(RotationProperty);
  }
  public static void SetRotation(DependencyObject element, float rotation)
  {
    element.SetValue(RotationProperty, rotation);
  }

  private static void OnRotationChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
  {
    Path path = d as Path;
    if (path != null)
    {
      var geometry = path.Data as StreamGeometry;
      if (geometry == null)
      {
        geometry = new StreamGeometry();
        path.Data = geometry;
      }

      using (var context = geometry.Open())
      {
        float rotation = GetRotation(path);
        // generate cool down geometry with current rotation value...
      }
    }
  }      
}

...
<Storyboard x:Key="CoolDownAnimation">
  <DoubleAnimation
    Storyboard.TargetName="CoolDownPath"
    Storyboard.TargetProperty="(local:CoolDownPathAnimation.Rotation)"
    From="0" To="360" Duration="0:0:5"/>
</Storyboard>
...
<Path x:Name="CoolDownPath" local:CoolDownPathAnimation.Rotation="0" Fill="#80000000"/>
...

         float angleRad = // provide your angle in radians
			float angleDeg = angleRad * (float)(180f / Math.PI);

			var w = this.width;
			var h = this.height;

			Vector2 point = new Vector2(w / 2 + (w * 2 * Mathf.Cos(angleRad)), h / 2 + (h * 2) * Mathf.Sin(angleRad));

			using (StreamGeometryContext ctx = this.clipGeometry.Open())
			{
				ctx.BeginFigure(new Point(w / 2, 0), true);
				ctx.LineTo(new Point(w / 2, h / 2));
				ctx.LineTo(new Point(point.X, point.Y));

				if (angleDeg < 45)
				{
					ctx.LineTo(new Point(w, 0));
				}

				if (angleDeg < 180)
				{
					ctx.LineTo(new Point(w, h));
				}

				if (angleDeg < 270)
				{
					ctx.LineTo(new Point(0, h));
				}

				if (angleDeg < 315)
				{
					ctx.LineTo(new Point(0, 0));
				}
			}
			// all done

                var rectangle = this.FindName("Rectangle").As<Rectangle>();
                this.clipGeometry = new StreamGeometry();
                rectangle.Clip = this.clipGeometry;