Let (sin⁡a)x2+(sin⁡a)x+1−cos⁡a=0 The set of values of a for which roots of this equation are real and distinct, is

The roots of the given equation will be real and distinct, iff sin2⁡a−4sin⁡a(1−cos⁡a)>0⇒(1−cos⁡a){1+cos⁡a−4sin⁡a}>0⇒2cos2⁡a2−8sin⁡a2cos⁡a2>0⇒2cos2⁡a2(1−4tan⁡a2)>0⇒4tan⁡a2<1⇒−π2