. . . . . . . . youth of Great Britain wants to have . . . . . . . . better life for . . . . . . . . British people.

In the first blank, article "the" will be used because "the" is used to refer to a particular/specific group of people.
In the second blank, article "a" will be used because the speaker is making a general statement.
In the third blank, article "the" will be used because article "the" is used to refer to a DEFINITE group of people like 'BRITISH PEOPLE'.