If 3−tan2⁡π71−tan2⁡π7=kcos⁡π7 then the value of k is

Let θ=π7⇒ 3θ=π−4θ⇒ sin⁡3θ=sin⁡4θ⇒ 3sin⁡θ−4sin3⁡θ=4sin⁡θcos⁡θcos⁡2θ⇒ 3−4sin2⁡θ=4cos⁡θ2cos2⁡θ−1⇒ 8cos3⁡θ−4cos⁡θ=4cos2⁡θ−1⇒ 4cos⁡θ2cos2⁡θ−1=4cos2⁡θ−1⇒ 4cos⁡θ=4cos2⁡θ−12cos2⁡θ−1=3−tan2⁡θ1−tan2⁡θ