#2sin^2theta-sintheta=0#
or, #sintheta(2sintheta-1)=0# [taking #sintheta# common from both sides]
now,either #sintheta=0# or #(2sintheta-1)=0#
we know the value of #sintheta# being #0# is #0# degree.so that rules out because the domain is #0 < theta < 360.#
now #(2sintheta-1)=0#
or #2sintheta=1#
so #sintheta=1/2#
the value of #sintheta# being #1/2# is #30# degree.
So the first value is #30#. This is in the first quadrant, but we know #sin theta# is positive in the second quadrant too. So we take #180# degrees. We can't take 90 degrees because that would change sin to cos. So now the equation is:
#sin30=sin(180-30)#
#sin30=sin150#
so this is the answer.
Answer: #sin30°#, #sin150°#
