A few extra comments to schielenkrahe's good advice.
For every old saying there is another, saying just the opposite. So for "good things come to those who wait" there is "fortune favours the bold." While I was undoubtedly lucky in getting my first contract, it wasn't dumb luck - it was being out there and getting myself noticed that did the trick.
That thereminists are rare can work to your advantage. I have noticed that a lot of players are members of more than one band. That's a smart move - every time one of the bands gets a gig, you get a gig. So get involved in the local music scene - go to gigs, buy the band a drink afterwards.
Offer a quality product. A persistent advertising campaign may get your foot in the door, but a weak gig will make sure you don't get a second performance.
There's an opportunity coming up in about three weeks time - Halloween. (I'll be playing to an audience of five year olds. That's cool - my friend Liz does the best kid's parties, she really goes the whole nine yards with decorations and costumes. How could she resist someone who plays the original spooky woo-woo box? I'll be devising an appropriate set, and it'll be a blast.)
Perhaps next year I'll be more confident and approach some local clubs and pubs for their All Hallows Ball. And I have a couple of friends in the local Am-Drams, so I could make sure they think of me when they do A Christmas Carol, or something in the sci-fi genre. Hmm. The more I think about it, the more opportunities there are. Maybe you could throw a party for all your new-found music-biz friends and let them persuade you to play.
Here's a neat one. Give people the opportunity to discover you! Record labels and event organisers are plagued with bands telling them how great they are. And most of them aren't. So they all get tarred with the same bush. Maybe one or two get listened to. But that's just dumb luck.
I wish I could claim it was intentional and carefully planned, but this was how I got my first gig. I emailed the organiser and asked her directions to an up-coming show. I think mentioning that I was looking at a satellite photo of the venue on Google Earth and was the car park across the road on the other side of the wall public or private? kind of caught her attention first, but it probably didn't hurt that I was using my theremin.org.uk email address and had a link to my mySpace site in my sig.
Bless her, she followed the link and "discovered" me. I wonder how many emails from bands claiming to be the best thing ever got completely ignored that day.
Oh, and don't forget that that the theremin is interesting from an educational point of view, both historically as the original electronic instrument and from it's hands-free mode of playing. Talk to your local schools and colleges.