Trigonometric equation question

Find all angles between 0 and 360 degree inclusive which satisfy the following equation,
2 * (cos 2x) ^2 = 3 / (cosec 2x)

please help me with the workings

2 * (cos 2x) ^2 = 3 / (cosec 2x)

2 * (cos 2x) ^2 = 3sin 2x

2 { 1 - ( sin 2x ) ^2 } = 3sin 2x........since ( cosx ) ^2 = 1- ( sinx ) ^2

now ( sin2x ) ^2 + 3 sin 2x - 2 = 0

2t^2 + 3t - 2 = 0 where t =sin 2x

( 2t - 1)( t + 2 ) = 0

thus t = 1/2 or -2

sin2x = 1/2 or - 2............sin 2x cannot be -2 as its range is from -1 to 1

therefore sin 2x = 1/2

2x = 30 , 150 , 360 + 30 , 360 + 150

x = 15 , 75 , 195 , 255 degrees

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