A value of θ lying between θ=0 and θ=π/2 and satisfying the equation1+sin2⁡θcos2⁡θ4sin⁡4θsin2⁡θ1+cos2⁡θ4sin⁡4θsin2⁡θcos2⁡θ1+4sin⁡4θ=0 is

Applying R1→R1−R3,R2→R2−R3 to the given determinant we get10−101−1sin2⁡θcos2⁡θ1+4sin⁡4θ=0⇒1+4sin⁡4θ+cos2⁡θ+sin2⁡θ=0⇒sin⁡4θ=−1/2⇒4θ=π+π/6 or 2π−π/6 [∵0<4θ<2π]⇒ θ=7π/24 or  11π/24