I think this is a really tough one to negotiate. You often find that line managers will agree to 4 days a week but find it tough to agree to 3.
What you need to do is detail how 40% of the role can effectively be covered or not done. This means having a really good view on your role, where you really add value and what they would not want to lose. What could be stopped e.g. are there certain meeting that you really do not need to attend. How could you develop some of your directs by delegating and use the 40% saving on your salary to promote them etc.
You need to detail what the potential impacts are on your boss, colleagues, your team and you. Then one by one explain how you will manage these or mitigate them. What will happen on the days you are not there?
You need to be realistic and look at the situation from your boss's perspective because that is how you will write the most compelling arguements.
Also, have you talked to your colleagues or directs about it? It can be useful to understand how they feel and work through stuff with them. If you can influence them and get them on side then you will have more chance of agreeing it.
Also, don't forget about the impact on you. I have one friend who thought 3 days was Nirvana, she returned on the agreement and hated it because she hated not being in control of all the elements of her role.
Things colleagues/line and directs will be concerned about:
Who will do the 40% that will not be done
What will happen to projects - will i have to do all of them because so and so can't do it
What about urgent queries?
How will we be able to answer stuff, find the info in x's absence?
Will I just be asked to do more to cover and not get anything for it.
Will less simply be delivered, (which may or may not be acceptable?
What happens to team meetings - will everything need to be scheduled around x
Will they take their fair share of extra work?
Are they going to become a 9 to 5 er?
NOw you may think the questions are mad but if you don't find a way of ackknowledging they are legitimate and answering them positively you will lessen your chances of a yes.
Also agree with Squiffy in that I think committing to either other solutions and being flexible is a must to get a yes.
Good luck