From my experience I can see that Project Manager/Team Leader is often responsible for many tasks not directly connected with his day to day job. For example he often takes part in sales meetings. On the other hand he has to persuade his team or his supervisors to some decisions and ideas. In many different situations he is speaking in front of the audience, which can be small but can contain decisive people from higher job positions than his own.

Should a project manager spend some time sharpening his public speaking skills? What is the best way to do it?