Skype’s new strategy for 2010: Your flat-screen TV in your living room can now be your phone. Or, if your tastes run more toward “The Twilight Zone,” think of it as your TV watching you — as you watch TV. The makers of popular software that allows users to make free phone and video calls via the Internet announced new deals Tuesday with LG and Panasonic that put Skype inside new Web-connected versions of their HDTVs. Starting sometime in mid-2010, consumers who buy certain Panasonic and LG sets will be able to plug in special webcams and enjoy face-to-face conversations.