CS1A September 2019 9(ix a)

I'm confused about this question. After calculating the confidence interval for theta, the rate parameter for a gamma distribution, it then asks

"Determine the variance of the distribution of theta at both lower and upper limits of the confidence interval calculated in part".

I didn't understand this at all. Reading the answer, what the question wanted was for us to use the formula for the variance of the gamma distribution worked out earlier, and just plug in the theta values from the confidence interval. However, the formula calculated earlier in the question for the variance (4*theta^2) was for the underlying gamma distribution, and was not referring to the distribution of theta (which was assumed to be approximately normal for calculating the confidence interval) which is obviously a parameter of that distribution.

But the question clearly stated distribution of theta which is not necessarily the same as the underlying distribution (in fact it is assumed not to be I think?). Am I missing something or is this question just terribly stated?

(I notice that the examiner comments state that this part of the question was poorly answered, can't say I'm surprised!)