Step-by-step explanation:

First, we have 2 tan 45°, which is 2 multiplied by the tangent of 45 degrees, which is 1. So, that term is simply 2.

Next, we have 4 sin 30°, which is 4 multiplied by the sine of 30 degrees, which is 1/2. So, that term is 2.

Then, we have √3 cos 30°, which is the square root of 3 multiplied by the cosine of 30 degrees, which is √3/2. So, that term is (√3/2).

Moving on, we have cos 60°, which is 1/2.

We also have sin 30°, which is 1/2.

Lastly, we have cot 45°, which is 1.

Now, let's substitute these values back into the expression:

2 - 2 + (√3/2) ÷ (1/2 + 1/2 + 1)

Simplifying further:

2 - 2 + (√3/2) ÷ 2

2 - 2 + (√3/2) ÷ 2

2 - 2 + (√3/2) ÷ 2

0 + (√3/2) ÷ 2

(√3/2) ÷ 2

Finally, let's simplify:

(√3/2) ÷ 2 = √3/4

So, the value of the expression is √3/4.