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Coordinating with teams from Dallas, Singapore, Thailand and Spain, __________ devised a solution that was simple and effective.
1.) "I" : I was the one who devised most of the solution. However, I think this makes me sound a little arrogant. And maybe this does not reflect teamwork.
2.) "we" : I was the project manager for the whole thing. So "we" makes sense in terms of teamwork. But I think I am missing a chance to demonstrate my abilities.
3.) "my team" : sounds good. teamspirited too. but again, I did the work !!!
depends what else you have said - is this for a CV or an application? If a CV, is your title for the job "Project Manager"?
Dependent on that, if no mention of project managing I would consider "Managed a project with a team based across three continents to complete x" or something similar. If you say you are a project manager, their is no need for the first bit, and can change it to a more general line.
Also, was it to budget and schedule? That is often considered a valuable side to project management. The solution should be effective, but is often late and over-budget.
As a general stand alone line I would make it clear that you managed the project, so there is no doubt in the role you played. To an extent I would make sure you at least start with a few details (value?) and definitely that it was to time, budget and specification.