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Solution

cos3x = -sqrt(3)/2

3x = cos^-1(-sqrt(3)/2)

3x = pi-pi/6 , pi+pi/6= 5pi/6 , 7pi/6

3x =5pi/6+ 2kpi ;

x = 5pi/18 + 2kpi/3

3x = 7pi/6 +2kpi

x = 7pi/18 + 2kpi/3

Solution in the interval [0, 2pi)

x= 5pi/18 ,(5pi/18 +2pi/3) , (5pi/18 +4pi/3)

= 5pi/18 , 17pi/18 , 29pi/18

= 7pi/18 , (7pi/18 + 2pi/3) , ( 7pi/18 +4pi/3)

= 7pi/18 , 19pi/18 , 31pi/18