sqrt ( 3 ) * csc ( 2 theta ) = - 2 Divide both sides by sqrt ( 3 )
csc ( 2 theta ) = - 2 / sqrt ( 3 )
Take the inverse cosecant of both sides.
2 theta = - pi / 3
2 theta = 4 pi / 3
[ Becouse csc ( pi / 3 ) = 2 / sqrt ( 3 ) , and csc ( 4 pi / 3 = 2 / sqrt ( 3 ) ]
Divide both sides by 2
theta = - pi / 6
theta = 2 pi / 3
Period of csc ( theta ) = 2 pi
So period of 2 theta = 2 pi / 2 = pi
Final solutions :
theta = n pi + 2 pi / 3 = pi ( n + 2 / 3 )
theta = n pi - pi / 6 = pi ( n - 1 / 6 )
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