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Evaluate the following: i) `sin pi/12` ii) `sin pi/8`, iii) `cos pi/8`, iv) `cos pi/(24`

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Evaluate the following: i) `sin pi/12` ii) `sin pi/8`, iii) `cos pi/8`, iv) `cos pi/(24`
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i) `(sqrt(3)-1)/(2sqrt(2)`, ii) `sqrt(2-sqrt(2))/(2)`, iii) `sqrt(2+sqrt(2))` , iv) `sqrt(4+sqrt(6)+sqrt(2))/(8)`
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