How do you solve this trigonometric equation?

Question

Find the solutions to the equation

#2##sin##theta##cos##theta##-##sin##theta# = #0#

#-180##<=##theta##<=##180#

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Answer 1 · 2018-01-18T12:45:45

#theta=-180^@,-60^@,0^@,60^@,180^@#

#2sinthetacostheta-sinteta=0#

#=>sintheta(2costheta-1)=0#

therefore either #sintheta=0# i.e. in the given interval #-180^@<=theta<=180^@#, we have #theta=-180^@,0^@,180^@#

or #2costheta=1# i.e. #costheta=1/2# and #theta=-60^@,60^@#

Hence #theta=-180^@,-60^@,0^@,60^@,180^@#