What is the best way to deal with a 2.5 year old throwing tantrums, especially in public? Will this be a phase that will pass?

Yes, this is only temporary. Don't worry. How long differs from individual. My kids also went through this. I pulled my kids to one area where it is not so many people and let them cry all they 1. Until they stop, then only I will talk to them. Speaking with them during this period would be more ideal.