Final answer:
The question seems to be about solving a trigonometric equation, but due to a typo or error in the equation provided, it is not possible to give a correct answer without further clarification. Typically, solving such an equation would involve isolating the variable and using inverse trigonometric functions.
Step-by-step explanation:
The question seems to involve solving for an angle based on an equation involving trigonometric functions. Specifically, finding the value that satisfies the equation −7sin(4) = 7 6, for which the options provided are π / 6, π / 3, 5π / 6, and 4π / 3. Unfortunately, there appears to be a typo or confusion in the presented problem, as the equation −7sin(4) = 7 6 does not seem to be complete or properly structured in terms of typical trigonometric equations. Moreover, the sequence of mathematical statements related to the trigonometric identities and theorems (such as laws of sines and cosines) seems to be provided for reference, but it does not directly address the given question.
To potentially solve the problem, it would be necessary to have a clear and correct equation. For example, if the question intended to find the angle where −7sin(θ) equals a certain value, one would isolate θ and then use inverse trigonometric functions to solve for it.