JTabbedPane with Keyevents

I have created a tabbedpane with 3 tabs (Tab1, Tab2, Tab3) . Mnemonic
(ALT-F) is assigned only to the Tab1.

If any of the component is selected inside the Tab2 or Tab3, it can
still traverse back to Tab1 on pressing key ALT-F.
But if any component is selected in the Tab1 itself, pressing ALT-F
will not take me back to Tab1. I have to somehow get the focus for
Tab1 too.

Here is my code. Please respond to this.
Thank you.

Note: I don't want to set Mnemonic to each Tab. Only one Mnemonic
should do my work.

import java.awt.BorderLayout;
import java.awt.event.KeyEvent;

import javax.swing.JButton;
import javax.swing.JCheckBox;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JTabbedPane;
import javax.swing.event.ChangeEvent;
import javax.swing.event.ChangeListener;

public class myClass {

    public static void main(String args[]) throws Exception {

        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

         JTabbedPane tabbedPane = new JTabbedPane();

        JButton button1= new JButton("Button1");
        JButton button2= new JButton("Button2");
        JPanel panel1 = new JPanel();
        panel1.add(button1);
        panel1.add(button2);

        tabbedPane.addTab("Tab1", null, panel1, null);

        JLabel label = new JLabel("Check ");
        JCheckBox cbox = new JCheckBox("check me");
        JPanel panel = new JPanel();
        panel.add(label, null);
        panel.add(cbox);

        tabbedPane.addTab("Tab2", null, panel, null);

        JButton button2 = new JButton("Button");
        tabbedPane.addTab("Tab3", null, button2, null);

         int mnemonic = KeyEvent.VK_F;
 
tabbedPane.setMnemonicAt(tabbedPane.getSelectedIndex(), mnemonic);

        ChangeListener changeListener = new ChangeListener() {
            public void stateChanged(ChangeEvent changeEvent) {

                JTabbedPane tab = (JTabbedPane)changeEvent.getSource();
                int index = tab.getSelectedIndex();

                if(index==0)
               tab.requestFocus();

              }
          };
          tabbedPane.addChangeListener(changeListener);

        frame.add(tabbedPane, BorderLayout.CENTER);
        frame.setSize(400, 150);
        frame.setVisible(true);

    }

}