Every mathematician has had the experience of being "scooped," and it's never a pleasant feeling. As you can see from the many upvotes, we all sympathize with your situation.
Objectively, though, the situation is probably nowhere near as bad as it might seem to you right now. As Zach Teitler mentioned in a comment, the fact that someone else has proved something very similar is a good sign that you have been working on, and building up expertise in, a field of some importance. That means you are well-prepared to make a significant contribution. The fact that your approach was original is also a good sign. I would say that it's not so important that your approach happened to be not as good in this particular case; ultimately, originality is harder to come by and more valuable than whether you happen to beat out someone else's method in a particular instance.
Also, while it may feel that you are throwing everything in the bin and starting over from scratch, this is probably not accurate. What you have learned, and the thought processes you have had, are likely to have enduring value. It is common in one's career to go back and revisit old territory, and succeed in an area where one had previously failed. I vividly remember one example when I was a graduate student and failed to prove a certain conjecture. Someone else proved the conjecture soon afterward, and that was a deflating experience. But I came back to the problem later and proved a much more general result using an improved version of my old ideas.
In short, don't blow this setback out of proportion. Your efforts have probably been much less "wasteful" than you think. Everyone experiences similar setbacks, and you will surely bounce back as long as you are able to get your emotions under control.