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`2sin^2(2x)=1`

`sin^2(2x)=1/2`

`sin(2x)=+-1/sqrt(2)`

General solutions for sin(2x)=-1/`sqrt(2)`

`2x=(5pi)/4+2pin, (7pi)/4+2pin`

`x=(5pi+8pin)/8 , (7pi+8pin)/8`

General solutions for sin(2x)=1/`sqrt(2)`

`2x=pi/4+2pin, (3pi)/4+2pin`

`x=(pi+8pin)/8 , (3pi+8pin)/8`

combine all the solutions ,

`x=(pi+8pin)/8 , (3pi+8pin)/8 , (5pi+8pin)/8 , (7pi+8pin)/8`

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`2sin^2(2x)=1`

`sin^2(2x)=1/2`

`sin(2x)=+-1/sqrt(2)`

General solutions for sin(2x)=-1/`sqrt(2)`

`2x=(5pi)/4+2pin, (7pi)/4+2pin`

`x=(5pi+8pin)/8 , (7pi+8pin)/8`

General solutions for sin(2x)=1/`sqrt(2)`

`2x=pi/4+2pin, (3pi)/4+2pin`

`x=(pi+8pin)/8 , (3pi+8pin)/8`

combine all the solutions ,

`x=(pi+8pin)/8 , (3pi+8pin)/8 , (5pi+8pin)/8 , (7pi+8pin)/8`

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