Creating a RegExp expression that limits the maximum input number to 2*pi radians (360 degrees) (in a Flutter app)

Question

I am building a Flutter app that has a textfield input, in which the user types an angle. There is a toggle that allows the user to change the unit between degrees and radians. The angle is related to compass directions, so I naturally want to allow a maximum input values of 360 degrees, or 2*pi radians. I have managed to build an expression that works for degrees, which looks like this:

r'^\b([0-2]?[0-9]{1,2}|3[0-5][0-9]|360)\b'

This expression allows whole numbers between 0 degrees and 360 degrees. If there's a way to modify this to allow decimals as well, that would be fantastic, although it isn't absolutely necessary.

Creating an expression that works when a user has toggled the input units to be radians is where I am struggling. Essentially, it needs to allow users to type in a number with up to two decimal places (or none at all) with a maximum of 6.28 radians. Below you can see what I have managed to put together so far:

r'^\b(6|([1-6])\.?|0\.[1-9]\d*)$\b'

As you will probably see straight away, this just doesn't work. I am aiming to allow users to input a value between 0 radians and 6.28 radians. I also want them to be able to type in a decimal number with no digit in front, such as .3 radians and to be able to type in a number with a decimal point but nothing after, such as 3. radians.

Can someone help me understand where I am going wrong with this? What should my RegExp expression look like, to cater for this? Thank you!