Let S be the sum of all solutions (in radians) of the equation sin 4 θ + cos 4 θ - sin θ cos θ = 0 in [ 0 , 4 π ] then 8 S π is equal to

Step-by-step solution

Given that: sin 4 ⁡ θ + cos 4 ⁡ θ − sin ⁡ θ cos ⁡ θ = 0    ;    θ ∈ [ 0 , 4 π ] ⇒ 1 − 2 sin 2 ⁡ θ cos 2 ⁡ θ − sin ⁡ θ cos ⁡ θ = 0 ⇒ 2 − sin 2 ⁡ 2 θ − sin ⁡ 2 θ = 0 ⇒ sin 2 ⁡ 2 θ + sin ⁡ 2 θ − 2 = 0 ⇒ sin ⁡ 2 θ = 1     ; 2 θ ∈ [ 0 , 8 π ] θ = &#96