Math: vertical viewing angle

I have a system in which I've worked out the code for giving an NPC a horizontal viewing angle (left image). How would I achieve a similar result, but now for the vertical direction (right image)?

Below is the code for the left image, for reference. This is a math question, thus the code isn't really necessary, but might help you understand the problem. Just ignore that the angles start from the NPC's center instead of his eyes, that's easy enough to fix. As you can see, the z-position is irrelevant for the horizontal viewing angle, but probably not for the vertical viewing angle (not sure).

static bool:FAI_IsPlayerInAggroViewingAngle(playerid, npcid) {
	// Get NPC position
	new Float:xn, Float:yn, Float:zn;
	FCNPC_GetPosition(npcid, xn, yn, zn);

	// Get player position
	new Float:xp, Float:yp, Float:zp;
	if(!IsPlayerNPC(playerid)) {
		GetPlayerPos(playerid, xp, yp, zp);
	} else {
		FCNPC_GetPosition(playerid, xp, yp, zp);
	}

	// Calculate the angle between these 2 points
	new Float:angleBetweenPoints = atan2(xp - xn, yp - yn);

	// Get the NPC facing angle adjusted for the weird GTA angle system
	new Float:npcFacingAngle = 360.0 - FCNPC_GetAngle(npcid);

	// Calculate the smallest difference between these 2 angles as a value between -180.0 and 180.0
	new Float:angleDifference = angleBetweenPoints - npcFacingAngle;
	if(angleDifference > 180.0) {
		angleDifference -= 360.0;
	}
	if(angleDifference < -180.0) {
		angleDifference = 360.0;
	}

	// Get the absolute value of this angle
	angleDifference = floatabs(angleDifference);

	// Check if the player is within the aggro viewing angle
	if(angleDifference <= FAI_NPCs/2) {
		return true;
	}
	return false;
}



Here's another visualisation of what the result should look like: