If θ is an acute angle and tan θ + cot θ = 2, then the value of tan2θ + cot2θ + 2 tan5θ cot4θ is :

3 4 1 2

4

tan θ + cot θ = 2 Here, tan θ = cot θ = 1 ⇒ θ = 45° tan2θ + cot2θ + 2 tan5θ cot4θ = 1 + 1 + 2 = 4