Discuss the concept of predetermined destiny and how it relates to the story of Romeo and Juliet.

Predestination and fate are very similar in concept, so a reader could use the two terms almost interchangeably.  Many readers feel that Romeo and Juliet were fated/predestined to end up committing suicide together.  That idea isn't exactly a big secret in the play either. Shakespeare is always dropping hints that Romeo and Juliet are going to soon die.  Look at the opening prologue.  

A pair of star-cross'd lovers take their life;

Shakespeare flat out tells his audience that an in love couple is going to die.  

That sense of a predetermined destiny oozes throughout the play as well.  Before Romeo crashes the Capulet party he says this:

I fear, too early: for my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night's revels and expire the term
Of a despised life closed in my breast
By some vile forfeit of untimely death.
But He, that hath the steerage of my course,
Direct my sail! On, lusty gentlemen.

In the above lines, Romeo is announcing that he has some misgiving feelings about the events that are about to be put into place.  It's almost like he can feel that he is being led down a path of destruction.  He feels like he is being "steered."  

Juliet isn't immune to dropping hints of her fated death either.  The first time that she sees Romeo, Juliet announces that her wedding bed will also be her deathbed.  

Go ask his name. The Nurse goes. If he be marrièd.
My grave is like to be my wedding bed.

This line works too for Juliet:

O God, I have an ill-divining soul!
Methinks I see thee, now thou art below,
As one dead in the bottom of a tomb.
Either my eyesight fails or thou look'st pale.

The above quotes are just some of the hints that Shakespeare continually drops throughout the play to emphasize the predetermined deaths of Romeo and Juliet.  It always amazes me that despite all of the hints at their deaths, audiences still are incredibly emotional when the deaths actually happen.  Audiences are still shocked that the two lovers died, despite the constant hinting.