In Hamlet, why does Hamlet attend the fencing competition when he knows his life is in danger?

You obviously need to look at Act V scene 2 to find the
answer to this question. After both Osric and the Lord have entered to tell Hamlet about
the impending fencing match with Laertes, Hamlet says to Horatio that in spite of all
the practice he has been doing, he still has an odd premonition that something is not
right about it, as he tells Horatio "how ill all's here about my
heart."

However, when Horatio gives him the opportunity to
get out of fighting the duel, Hamlet disagrees, giving the following speech as his
reason:

Not a
whit, we defy augury; there is special providence in the fall of a sparrow. If it be
now, 'tis not to come: if it be not to come, it will be now: if it be not now, yet it
will come; the readiness is all, since no man has aught of what he
leaves.

Note the tone of this
speech, which seems to show almost defiance in the face of whatever fate can throw at us
as humans. Hamlet, finally, seems to have reached a stage in the play where he is able
to demonstrate radical acceptance of whatever happens, even if that means his death.
Even in the death of a sparrow, there is "special providence," and it is clear that he
has accepted his death is inevitable anyway, so in one sense it makes little difference
if he dies now or later. At last we finally seem to be presented with a Hamlet who is at
peace with himself and with his future. This is why he duels with Laertes in spite of
his premonitions.