If cot^2 θ + cot^4 θ = 2, then the value of 2sin^4θ + sin^2 θ is :

cot²θ  + cot4 θ = 2

cot²θ ( 1 + cot²θ ) = 2

Using,

cosec²θ - cot²θ = 1

cot²θ (  cosec²θ ) = 2

\(\frac{cos²θ}{sin4 θ}\) = 2

cos²θ = 2sin4 θ

Now,

2sin4 θ + sin²θ

= cos²θ + sin²θ

= 1      { cos²θ + sin²θ  = 1 }