The Right Answers

Use the Double Possibility strategy for BOTH blanks. Occasionally, you will come across a text completion problem where the individual blanks cannot be completed individually. They are a "package." In most cases, two pairs of answer choices are possible. This is one of those cases.

Using Math Strategy, we can confirm that the two ideas support each other because of the phrase "in that."

Possible Pair 1
- normal / use: If her approach was "normal", she would "use" the theatrical devices normally used.
Possible Pair 2
- unconventional / rejects: If her approach was "unconventional," she would "reject" the theatrical devices normally used.

It must be stated that, despite all of our logic work, we do NOT know which pair is the correct answer. For that, we have to go to the answer choices. In looking at the answer choices, the best fit for blanks 1 and 2 are startling and jettison, matching our second possible pair of unconventional / rejects.

The Wrong Answers

Blank 1

pedestrian: This answer might have worked had we had a word like "use" in the answer choices of blank 2. Because we don't, we have to eliminate it.
celebrated: This answer choice has no evidence. The sentence gives us no indication if outside observers enjoy her works or not.

Blank 2

experiment with: This answer is a pretty good trap answer. If someone is "experimenting with" the theatrical devices normally used, then that person is arguably creating something new and innovative, which might match with blank 1's correct answer of "startling." The problem with this answer choice, however, is that if you're "experimenting with" the theatrical devices, you are still by definition using them -- so it's not all that "startling" to be honest.
distill: I would argue that this answer is wrong from a usage point of view. What does it mean to "distill" theatrical devices? Makes no sense to me.