1. Find all sets of four real numbers x1,x2,x3,x4 such that the sum of any one and the product of the other three is equal to 2.
2. Prove that cos(π/7) - cos(2π/7) + cos(3π/7) = 1/2 .
3. Solve the equation
cos^n{x} - sin^n{x} = 1
where n is a given positive integer.
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