Convert values form Sensor.TYPE_ORIENTATION to Euler angles?

Question

I have to write a compass app in Android. The only thing the user sees on the screen is a cube with a red wall which has to point north. This is not important. What's important is that I need to rotate that cube accordingly to the rotation of the device itself so that the red wall continues to point north no matter how the phone is being held. My code is simple and straightforward:

@Override
public void onSensorChanged(SensorEvent event) {
    synchronized (this) {
        switch (event.sensor.getType()){
        case Sensor.TYPE_ACCELEROMETER:
            direction = event.values[2];
            break;
        case Sensor.TYPE_ORIENTATION:
            if (direction < 0) {
                angleX = event.values[1];
                angleY = -event.values[2];
                angleZ = event.values[0];
            } else {
                angleX = -event.values[1];
                angleY = -event.values[2];
                angleZ = event.values[0];   
            }
            break;
        }
    }
}

I have added this extra direction variable that simply stores whether the phone's display is pointing downwards or upwards. I don't know if I need it but it seems to fix some bugs. I am using the SensorSimulator for android but whenever my pitch slider goes in the [-90, 90] interval the other variables get mixed up. It's like they get a 180 offset. But I can't detect when I am in this interval because the range of the pitch is from -90 to 90 so I can move that slider from left to write and I will always be in that interval.

This was all just to show you how far has my code advanced. I am not saying how this problem should be solved because I will only probably stir myself into a dead end. You see, I have been trying to write that app for 3 days now, and you can imagine how pissed my boss is. I have read all sorts of tutorials and tried every formula I could find or think of. So please help me. All I have to do is know how to rotate my cube, the rotation angles of which are EULER ANGLES in degrees.