Trig Equation Solving! HELP ASAP

Find all solutions in [0,2pi)

sin(x+pi/6)-sin(x-pi/6)=1/2



7csc2x-4=-18



Please show work and explain! Trying to study for my test! Thanks a ton!:))

sin(x + π/6) = sinxcos(π/6) + sin(π/6)cosx

sin(x - π/6) = sinxcos(π/6) - sin(π/6)cosx

=> sin(x + π/6) - sin(x - π/6) = 2sin(π/6)cosx = cosx

i.e. cosx = 1/2

=> x = π/3 and 5π/3
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cosec2x = -2

=> sin2x = -1/2...........as cosec2x = 1/sin2x

so, 2x = -π/6, 7π/6, 11π/6, 19π/6, 23π/6

i.e. x = 7π/12, 11π/12, 19π/12 and 23π/12

:)>

1) 2cos x sin(pi/6) = 1/2
cos x = 1/2
x = pi/3, 5pi/3

2) csc2x = -2
sin2x = -1/2
x = 7pi/12, 11pi/12, 19pi/12, 23pi/12