Here's an example Java program to calculate the union of two sets using the built-in Set data structure and the addAll() method:

import java.util.HashSet;
import java.util.Set;

public class SetUnionExample {
    public static void main(String[] args) {
        // Create two sets of integers
        Set<Integer> set1 = new HashSet<Integer>();
        Set<Integer> set2 = new HashSet<Integer>();

        // Add elements to the sets
        set1.add(1);
        set1.add(2);
        set1.add(3);

        set2.add(2);
        set2.add(3);
        set2.add(4);

        // Calculate the union of the sets
        Set<Integer> union = new HashSet<Integer>(set1);
        union.addAll(set2);

        // Print the union
        System.out.println("Set1: " + set1);
        System.out.println("Set2: " + set2);
        System.out.println("Union: " + union);
    }
}

This program creates two sets of integers, adds elements to them, and then calculates the union of them using the addAll() method. The result is a new set that contains all the elements from both set1 and set2, with no duplicates.

The output of the program will be:

Set1: [1, 2, 3]
Set2: [2, 3, 4]
Union: [1, 2, 3, 4]