I've bought this veeery cheap camera made in china, and obviously it lacks an angular holder for my hat...
Luckily I'm a real genius, and after a long research and a lot of examinations, diagrams, computer simulations and testing I've came to the design of this high technological piece of engineering! With that gear I'm able to make my camera looking forward!! That's extraordinary!
... all right, I'm kidding, but because I'm not able to abandon a project halfway through, I'll go on ;-)

Step 1:

About the camera I can't say here that it's a pitiful piece of technology, so please ask me in pm... whoops!! Anyway I never expected GoPro abilities for 1/30 of its price...
Oddly as you can see I've two holders for the camera, but neither of the two can be mounted on the cap in the right direction. Except screwing the base of the bigger one on the cap peak... but I don't want it permanent.

Step 2:

So I decided to keep the clamp connector and holder, but change the angle between them.
To do that I've cut a piece of plastic frame about one and half inch long.

Step 3:

Dismantling the clamp you'll retrieve one bolt with nut, the second one comes from the other camera holder.
You can use a bit made for the electric screwdrivers, which is easy to keep in hand and to turn. Make tho holes about at the same distance from the borders.

Step 4:

Now screw the bolts and the nuts together, and glue them with some cyanoacrylate glue, so they'll not slack.

Step 5:

Now try the clip on the hat, and insert your camera on that. As you can see it will allow you to change the inclination both on longitudinal and traversal axes, so you can direct the camera forward.

Step 6:

Enjoy your excursions and rides, but much probably you can use it to film your instructables and diy works, because of the narrow field of view and lacking of stabilization.
I hope you had funny ;-)