If cot67θ + tan133θ = 2, find sin2θ + 2cosθ.

If cotⁿθ + tanⁿθ = 2 then cotθ = tanθ = 1 where θ = 45°

Now,

⇒ sin2θ + 2cosθ = 1 + 2 × (\(\frac{1}{√2}\)) 

= 1 + √2