This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
If you mark a static method synchronized, it synchronizes on the class. A thread entering one of these prevents another thread entering any other such method.
If you mark a normal method synchronized, it synchronizes on the instance. So two threads can run the method at the same time if they're called on different objects, but on the same object only one synchronized method can be called at a time.
Your method3 example is a long-hand way of doing exactly the same as marking the method synchronized. This gives you more flexibility because:
a) You can synchronize on any object you want
b) You can synchronize only part of the method body, if you want
If you don't need this flexibility, just use the short-cut of marking the method.