The complex numbers sin x + i sin 2x and cos x - i sin 2x are conjugate to each other, for

Let z1=sin⁡x+icos⁡2x and z2=cos⁡x−isin⁡2x.Then z¯1=z2⇒ sin⁡x−icos⁡2x=cos⁡x−isin⁡2x⇒ sin⁡x=cos⁡x and cos⁡2x=sin⁡2x⇒ tan⁡x=1 and tan⁡2x=1⇒ x=π4 and x=π8This is not possible. Hence, there is no value of x.