How to determine turret rotation direction if rotation angle has to be limited, and target "passed behind"? - unity3d

Question

I started some programming in Unity just for fun a couple days ago.
So far my game (pretty much top-down shooter) consists of player flying in an asteroid field, in which lurk enemy ships. Player can shoot down asteroids and enemies, and enemy ships have missile turrets that "track" player.
Everything works fine until I decided that enemy ships shouldn't be able to rotate their turrets all the 360-way. Think of it as real-world battleship being unable to turn it's front turret (No.1) 180 degrees behind because turret No.2 is in the way.
Currently code for turret rotation is like this (this is not about making "gradual rotation", setting "rotation speed" or something, so please don't look at that!):
playerTarget = GameObject.FindGameObjectWithTag("Player");
chaseDirection = Quaternion.LookRotation(playerTarget.transform.position - transform.position);
newYaw = Mathf.Clamp(chaseDirection.eulerAngles.y, minYaw, maxYaw);
transform.rotation = Quaternion.Euler(0, newYaw, 0);
That works okay, until player flies behind enemy ship. As soon as player gets into turret's "possible rotation angle", it just snaps past "dead zone" to new direction if I don't turn it gradually with fixed angle, or is still stuck trying to rotate "past limit" until target (player) flies all around enemy ship so the angle to target is small enough for rotation direction to be calculated through "enabled" rotation zone, not through "dead zone".
An important thing is I am not looking for answer "how to make gradual rotation". I am looking about calculating rotation direction!
I thought about coding enemy to start rotating turret in counter-direction as soon as player passes "directly behind" the turret "forward facing" position. But the concept of how to do that eludes me.
Because as soon as turret rotates just a bit from limit, it's able to turn "towards" player again, and gets stuck at limit again.

Answer 1

Edited with the clarification in mind.
You need a function that will tell you if you should rotate clockwise or counter-clockwise, based on the enemy location.
First find the mid point, this will be:
var mid = (minYaw + maxYaw) / 2
In your example this will be 3 o'clock, straight right.
Now, if your current rotation is lower than mid, and the target is higher than mid, than you must rotate clockwise even if it's not the shortest rotation to get there.
If the target rotation is higher than mid, and the target is lower than mid, you must rotate counter-clockwise for the same reason. You may need to adjust for negative degrees.
Please note that this will create a secondary effect, where once the ship passes the half point of the dead zone (say moving from 10 o'clock to 8 o'clock in your example), the turret will start moving as if anticipating the flank. You may want to disable this movement in a special case.
I'll keep the second part of my answer as-is, for future references.
If you want it to move gradually, you need to use deltaTime or fixedDeltaTime in case of a fixed update. You can define how fast it will move by adding a speed property. Try something like this:
void update () {
var playerTarget = GameObject.FindGameObjectWithTag("Player");
var chaseDirection = Quaternion.LookRotation(playerTarget.transform.position - transform.position);
var newYaw = Mathf.Clamp(chaseDirection.eulerAngles.y, minYaw, maxYaw);
var currentRotation = transform.eulerAngles;
var desiredRotation= currentRotation;
var desiredRotation.y = newYaw;
transform.eulerAngles = Vector3.RotateTowards(currentRotation, desiredRotation, Time.deltaTime * RotationSpeed, 0.0f);
}