Java: Obtaining unique values from a list

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Java

I know there are classes like hashset that can remove duplicates but I doubt I can apply it to my case.
I have a list of dates, separated into month and day respectively.

private static List<MonthDay> Dates() {
		List<MonthDay> dates = new ArrayList <MonthDay>();
		dates.add(MonthDay.of(JAN, 1));
		dates.add(MonthDay.of(JAN, 2));
		dates.add(MonthDay.of(FEB, 3));
		dates.add(MonthDay.of(MAR, 1)); 
                return dates;
}

I've also created a method to return lists of specified dates.

private static List<MonthDay> Month(Month month) {
    List<MonthDay> monthList = new ArrayList<>();
    for (MonthDay m : Dates()) {
        if (m.getMonth().equals(month)) {
            monthList.add(m);
        }
    }
    return monthList;
}

Now, I want to have a method to check whether my month is unique or not, and then return a <monthday> list of the dates containing the unique months.
e.g. FEB and MAR are unique months in the list, so the output I should get is [--02-03, --03-01]

How do I go about doing so?