Hi I have problem with a normal calculation, I've worked for hours on it, but I don't get to the right calculation

What I want to do is interpolating between several textures depending on normalized world angle. For example at 0° there is texture1 visible (texture colour is multiplayed with Normal), at 90° there is texture2 visible and at 45° there would both being multiplayed with a value of sin(45) (Normal value of the angle). As you can see it would be very easy with 4 textures. Every texure would have a range of 180° and being multiplayed with the Normal of the angle.

But I want it to work with 8 textures and every texture has a range of 90°. So at 0° there is texture1, it fades out as the normal.x gets lower, at 45° (Normal value is sin(45)),it has to be 0, and texture2 has to be fully visible and so on.