Run an attached application and just move slider.

import javafx.application.Application;
import javafx.collections.FXCollections;
import javafx.collections.ObservableList;
import javafx.scene.Scene;
import javafx.scene.chart.PieChart;
import javafx.scene.control.Slider;
import javafx.scene.layout.Pane;
import javafx.stage.Stage;

public class JavaCharts extends Application {

    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage stage) throws Exception {
        ObservableList<PieChart.Data> data;
        data = FXCollections.<PieChart.Data>observableArrayList();
        for (int i = 0; i < 10; i++) {
            data.add(new PieChart.Data("Data item " + i, i * 100));
        }
        PieChart chart = new PieChart(data);
        chart.setTitle("PieChart");
        chart.setStyle("-fx-border-color: darkgray;");
        chart.setPrefSize(300, 600);

        Pane pane = new Pane();
        pane.getChildren().add(chart);
        
        Slider slider = new Slider(0, 300, 300);
        slider.setShowTickLabels(true);
        slider.setShowTickMarks(true);
        slider.valueProperty().bindBidirectional(chart.startAngleProperty());
        pane.getChildren().add(slider);
        
        pane.setPrefSize(600, 600);
        Scene scene = new Scene(pane, 700, 700);
        stage.setScene(scene);
        stage.show();
    }
}


You can see it on the attached movie. During movie I changed pref width and height, to set some size, and started to change start angle. You may see, that for some values, labels periodicaly intersect borders of control, which are marked with grey color.