Final answer:
The question appears to involve finding the maximum value of a trigonometric expression, but due to typographical errors and missing context, it cannot be accurately solved without further clarification.
Step-by-step explanation:
The student's question appears to be about maximizing the expression (2 sin 20 - 3 cos 20 + 3) to the power of 2. It seems like there is a typographical error in the question, and it might be referring to using sine and cosine identities to simplify and find the maximum value of this trigonometric expression. However, without the proper context or clarification on whether '20' refers to degrees or is a typographical error, and what 'e' stands for in '3sin e,' it is not possible to proceed with an accurate solution. An approach in a more general sense would involve using trigonometric identities to simplify the expression first and then applying calculus if necessary to find maximum values.