Hello from MrBillDoesMath!
Answer:
"He plans to sell the carrots for $5 per bunch..." is not needed
Discussion:
The question asked is "About how many bunches will the farmer make? The text "He plans to sell the carrots for $5 per bunch..." is not needed as it does not relate to the question asked.
Regards,
MrB
Answer: 
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Work Shown:
Apply the following trig identity

Now let's rationalize the denominator

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As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.
Or you can note how

which helps us see that they are the same thing.
Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as
but it's the same as above.
Hi there!
From the given information, we can infer that the inner quadrilateral has equal side lengths of x and 2x-3.
We can turn this into a mathematical equation with 1 variable.
x = 2x - 3
Subtract both sides by 2x
-x = -3
Multiply both sides by -1
x = 3
Have an awesome day! :)
~collinjun0827, Junior Moderator