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We need to relate the given information to what is required. Cubing both sides of the equation won't help because it will ultimately give us ,
which is not what we are required to determine.
We will therefore start by factorising ,
which is the sum of two cubes.
We can simplify the second set of brackets using the square identity:
In order to find the value of , we will now need to determine the value of and .
We can relate the two latter expressions through the square identity .
We were given that , so we can use the square identity again, only this time we will square .
We can now determine the value of :
Finally, we can evaluate :
Notes: The principles involved in this problem were essentially polynomial multipication, factorisation, and knowledge of trigonometric square identities. A fair bit of manipulation and some lateral thinking was also required. It goes without saying that the principle of BODMAS needs to be adhered to as well.
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