Let f:(−1, 1)→R be such that f(cos⁡ 4θ)=22−sec2⁡ θfor θ∈0,π4∪π4,π2. Then the value(s) of f13 is(are)

For θ∈0,π4∪π4,π2Let cos⁡ 4θ=13⇒ cos⁡ 2θ=±1+cos⁡ 4θ2=±23f13=22−sec2⁡θ=2cos2⁡θ2cos2⁡θ−1=1+1cos⁡2θ⇒ f13=1−32 or 1+32