C1→C1+C2+C3∣∣
∣
∣∣2+4sin4xcos2x4sin4x2+4sin4x2−sin2x4sin4x2+4sin4xcos2x1+4sin4x∣∣
∣
∣∣=0⇒(2+4sin4x)∣∣
∣
∣∣1cos2x4sin4x11+cos2x4sin4x1cos2x1+4sin4x∣∣
∣
∣∣=0R1→R1−R3, R2→R2−R3⇒(2+4sin4x)∣∣
∣∣00−101−11cos2x1+4sin4x∣∣
∣∣=0⇒(2+4sin4x)×1=0⇒sin4x=−12=−sinπ6⇒sin4x=sin(π+π6) or sin(2π−π6)⇒4x=2πn+7π6 or 4x=2πn+11π6⇒x=πn2+7π24 or x=πn2+11π24⇒x=7π24,11π24,19π24,23π24⇒Number of solutions is 4