How do I convert quaternion values to specific angles - angle

Question

I'm getting quaternion values, and I want to convert these values to 2 angles.
One of the angles is between the "ground plane" (please correct me if this is an incorrect name for it) and the fictional vector between the origin and the quaternion point ( the complementary angle of gamma ).
The second angle is the rotational angle, this is the rotation that the vector has made relatively to a plane perpendicular to the vector ( R in the picture ).
I looked lot up on the internet, but everything I try has a range of -90° to 90°, while I want it to go from -180° to 180°.
This is the last version of code I ended up with:
float gx = 2 * (x*z - w*y);
float gy = 2 * (w*x + y*z);
float gz = w*w - x*x - y*y + z*z;
float yaw = atan2(2*x*y - 2*w*z, 2*w*w + 2*x*x - 1); // about Z axis
float pitch = atan(gx / sqrt(gy*gy + gz*gz)); // about Y axis
float roll = atan(gy/gz); // about X axis
Serial.print(" yaw ");
Serial.print(yaw * 180/M_PI,0);
Serial.print(" pitch ");
Serial.print(pitch * 180/M_PI,2);
Serial.print(" sideways ");
// Don't mind this section as I'm applying a mathematical function I created
if(pitch > 0) Serial.println((roll * 180/M_PI) * (1/(1+pow(1.293,((pitch * 180/M_PI)-51.57)))), 2);
else if(pitch == 0) Serial.println(roll * 180/M_PI, 2);
else if(pitch < 0) Serial.println((roll * 180/M_PI) * (1/(1+pow(1.293,(((pitch) * (-180)/M_PI)-51.57)))), 2);

Answer 1

You should always use atan2(y,x) instead of atan(y/x). It is a common mistake. – Somos
He wrote this on a math form were I asked this too, and that was my stupid mistake -_-
My new version is:
float gx = 2 * (x*z - w*y);
float gy = 2 * (w*x + y*z);
float gz = w*w - x*x - y*y + z*z;
float yaw = atan2(2*x*y - 2*w*z, 2*w*w + 2*x*x - 1); // about Z axis
float pitch = atan2(gx, sqrt(gy*gy + gz*gz)); // about Y axis
float roll = atan2(gy, gz); // about X axis
/*Serial.print(" yaw ");
Serial.print(yaw * 180/M_PI,0);*/
Serial.print(" pitch ");
Serial.print(pitch * 180/M_PI,2);
Serial.print(" sideways ");
// Please don't pay attention to the extra function I made for the project but it doesn't have to do with the problem
if(pitch > 0) Serial.println((roll * 180/M_PI) * (1/(1+pow(1.293,((pitch * 180/M_PI)-51.57)))), 2);
else if(pitch == 0) Serial.println(roll * 180/M_PI, 2);
else if(pitch < 0) Serial.println((roll * 180/M_PI) * (1/(1+pow(1.293,(((pitch) * (-180)/M_PI)-51.57)))), 2);