#2sin (2x - pi/3) = - 1#
#sin (2x - pi/3) = - 1/2#
Trig table and unit circle give 2 solutions for #(2x - pi/3)#
a. #(2x - pi/3) = - pi/6 + 2kpi#
#2x = - pi/6 + pi/3 = pi/6 + 2kpi#
#x = pi/12 + kpi#
k = 0 --> #x = pi/12# ; k = 1 --> #x = 13pi/12# ;
b. #2x - pi/3 = pi - (-pi/6) = (7pi)/6 + 2kpi#
#2x = (7pi)/6 + pi/3 = (9pi)/6 + 2kpi = (3pi)/2 + 2kpi#
#x = (3pi)/4 + kpi#
k = 0 --> #x = (3pi)/4#; k = 1 --> #x = (7pi)/4#
Answers for (0, 2pi) -->
#pi/12; (3pi)/4 ; (13pi)/12 ; (7pi)/4#
Answers for #(-2pi, 0)#
#(-23pi)/12; - (5pi)/4 ; - (11pi)/12 ; - (pi/4)#
Note.
#(-23pi/12)# is co-terminal to #(pi/12)#
#(-5pi)/4# is co-terminal to #(3pi)/4#
#(-11pi)/12# is co-terminal to #(13pi)/12#
#(-pi/4)# is co-terminal to #(7pi)/4#
