Is Romeo fortune's fool? Can you please use evidence from Act III, Scene 1, lines 114-142.

Act III, Scene 1 of Romeo and Juliet is called the turning point in the play because it propels the plot toward the ultimate tragedy of the young lovers' double suicide. Fate, or the idea that certain things in life are already determined for us, is an integral aspect of the play. From the outset in the Prologue, Shakespeare tell us that Romeo and Juliet are "star-crossed lovers", meaning that fate, or fortune, will intervene in their lives. 

Later in Act I, Scene 4, Romeo again invokes the shadow of fate when, in an aside, he says,

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 despisèd life closed in my breast
By some vile forfeit of untimely death.

At this point Romeo is well aware that his course in life and his mortality are being manipulated and he is at the whim of fate, well before he even lays eyes upon Juliet.

In the opening of Act III, Benvolio warns Mercutio that they should get off the street because it's a hot day and tempers may boil over if they meet the Capulets. Mercutio ignores Benvolio and, not surprisingly, is soon fighting Tybalt over a supposed slight against Romeo. Tybalt has actually come to fight Romeo, but since he has recently married Tybalt's cousin in a secret ceremony, Romeo backs down, giving vague responses to Tybalt's challenge. Romeo says in lines 63-66,

Tybalt, the reason that I have to love thee
Doth much excuse the appertaining rage
To such a greeting. Villain am I none.
Therefore farewell. I see thou knowest me not.

Mercutio cannot accept Romeo's acquiescence, so he draws on Tybalt and the two fight. An excellent portrayal of this duel can be found in Zeffirelli's 1968 movie version of the play. The fight is not meant to go to the death, but Romeo, worried about the Prince's edict from earlier, tries to part the two and Mercutio is mortally wounded under Romeo's arm. In line 114 Romeo admits his culpability in the wounding of his friend and says, 

My very friend, hath got this mortal hurt
In my behalf. My reputation stained
With Tybalt’s slander—Tybalt, that an hour
Hath been my cousin! O sweet Juliet,
Thy beauty hath made me effeminate
And in my temper softened valor’s steel.

And even though Romeo must know that further violence could jeopardize his life and his marriage to Juliet, he invokes fate when he vows to avenge Mercutio's death and pursue Tybalt. He says, in lines 124-125,

This day’s black fate on more days doth depend.
This but begins the woe others must end.

After Romeo kills Tybalt, he is brought back to his senses and realizes he has once again been manipulated by fate. As Benvolio urges him to flee, Romeo says, "O, I am Fortune’s fool!" And indeed he is. His actions bring banishment and finally his death.