#3cscx-2sqrt3=0#
Add #2sqrt3# to both sides
#3cscxcancel(-2sqrt3)cancel(+2sqrt3)=cancel(0+)2sqrt3#
#3cscx=2sqrt3#
Divide both sides by #3#
#(cancel3cscx)/cancel3=(2sqrt3)/3#
#cscx=(2sqrt3)/3#
Replace #cscx# with #1/sinx# and #sqrt3/3# with #1/sqrt3#
#1/sinx=2/sqrt3#
Raise both sides to the power of #"-"1# and simplify
#(1/sinx)^("-"1)=(2/sqrt3)^("-"1)#
#sinx=sqrt3/2#
Use knowledge of special angles (or a calculator if you don't need an exact answer)
#x=pi/3#
Realize that #sin(pi-theta)=sin(theta)#
#x=pi/3,(2pi)/3#
Since #x# is unbounded and #f(x+2npi)=f(x)# when #f(theta)# is a trig function and #ninZZ#
#{x:x=pi/3+2npi,(2pi)/3+2npi;ninZZ}#
