In Hamlet, explain the irony in the King's declaration, "How much I had to do to calm his rage."

This quote is part of the final comments by King Claudius
at the end of Act 4.  Laertes has stormed back to Elisinore demanding vengeance for his
father's murder.  Claudius has been kept VERY busy in these scenes with Laertes trying
to first calm him down, then deflect responsibility from himself to Hamlet, commiserate
over the insanity of Ophelia, convince Laertes to hatch a plot against Hamlet, and
finally console the bereaved Leartes upon hearing that his sister had drowned
herself. Claudius probably heaves a huge sigh of relief that he survives the act at
all!

When Laertes first returns to Elsinore he lays the
blame for his father's death more on Claudius than Hamlet, because while Hamlet did the
act, Claudius should take some responsibility for keeping control of his seemingly crazy
step-son.  Laertes is furious when he first enters the room and wants to blame anyone
who will listen, but Claudius assures him that "I am guiltless of your father's death /
And am most sensibly in grief for it."  He no more than delivers these words,
when Ophelia, who has lost her mind from grief, enters the room in a clear state of
madness.  She talks to each person in the room, but makes little sense.  Laertes is
devastated to see his sister like this, and blames Hamlet for his part in destroying her
through his treatment of her as well as the fact that he killed their father.  Again,
Claudius has to talk Laertes down with assurances that he is as upset as Laertes over
this turn of events and says that "we shall jointly labor with your soul / To give it
due content."  He means that he will do whatever he can to make Laertes feel that
justice has been served in this case.  Claudius agrees that Hamlet will have to pay with
his life.  What is ironic is that this is EXACTLY what Claudius wants.  He is already
actively planning to have Hamlet killed while doing official business in
England.

Claudius tries to explain why he didn't take a
stronger hand with Hamlet -- that he was beloved of the people and of Gertrude, but
assures him that things will change now.  He no sooner delivers this promise when a
messenger arrives with the note from Hamlet announcing that he has returned in secret
from England.  Laertes is aroused to anger again and boldly states that this news "warms
the very sickness of my heart."  Leartes agrees to be "ruled" by Claudius and go along
with a plan against Hamlet as long as "you [Claudius] will not o'errule me to a peace." 
He wants vengeance, not concessions. 

As the scene
progresses, Laertes and Claudius hatch their plan to draw Hamlet into a sword fight
where they will have a poisoned and sharpened sword as well as a cup of poisoned wine. 
Just when Claudius can think he can be pleased with his fine manipulation of Laertes to
do Claudius's "dirty work," news arrives that Ophelia has committed suicide.  This
pushes Laertes to fury again, but Claudius calms him down by reminding him that they
have a fool-proof plan to bring Hamlet to justice.  Claudius feels very lucky that he
has been able to control and maneuver Laertes into this plan by the end of Act 4, but it
has been a lot of hard work and smooth talking that let him achieve those ends.  The
ultimate irony is that all of these events have been set in motion because of Claudius's
murder of King Hamlet in the first place!