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if cos^(-1)((1)/(sqrt(2))(cos((7pi)/(5)-...

if `cos^(-1)((1)/(sqrt(2))(cos((7pi)/(5)-sin((2pi)/(5)))=(ppi)/(q)` (where p,q are in lowest form), then value of `(q-p)` is

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The correct Answer is:
3
`cos^(-1)((1)/(sqrt(2))(cos((7pi)/(5))-sin((2pi)/(5)))`
`=cos^(-1)(cos((2pi)/(5))cos((3pi)/(4))-sin((3pi)/(4))sin((2pi)/(5)))`
`=cos^(-1)(cos((23pi)/(20)))=(2pi-(23pi)/(20))=(17pi)/(20)`
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