How and why does Othello suddenly threaten Iago in Shakespeare's Othello?Act III, Sc. 3

Othello's threat may seem sudden, but Iago's cruel
torments have been working away at his master's soul to the point that he can take no
more.

Initially, Iago raises Othello's suspicions of Cassio
by simply returning Othello's words, implying he feels his comments would be too
indelicate-

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OTHELLO:

Think,
my lord? By heaven, he echoes me,
 As if there were some monster in his
thought 
 Too hideous to be
shown.

Iago then directs
Othello to consider whether he trusts his wife, having warned him of the evils of
jealousy-

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I speak not yet of
proof. 
Look to your wife; observe her well with
Cassio

Wear your eye thus, not jealous nor
secure. 
 I would not have your free and noble nature 
 Out of
selfbounty be abused. Look
to't.

 Iago is leading
Othello, as he indicated he would , to his own downfall. Iago has sworn to bring down
Othello and Desdemona.

Othello’s anger builds and he
threatens Iago-

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Villain, be sure thou prove my love a whore;

Be sure of it. Give me the ocular proof;
Or, by the worth of man's
eternal soul,
Thou hadst been better have been born a dog
Than
answer my waked
wrath!

Othello’s passionate
temper is tragic in that the audience already know that Iago has Desdemona’s
handkerchief, and has long conceived of a plan to use it in his cruel deception. The
audience realises that Iago will do as Othello asks, and is likely to succeed in his
devilish plan.