Verified answer

∫(CSC2θ-COT2θ)2 dθ.

If the '2' after the bracket and before 'dθ' is to be taken as 'square' and limits in Radians;

∫(CSC2θ-COT2θ)^2 dθ

= ∫(1/Sin2θ - Cos2θ/Sin2θ)^2 dθ

= ∫([1 -Cos2θ]/2SinθCosθ)^2 dθ

= ∫([Sin^2 θ]/Sinθ Cosθ)^2 dθ

= ∫([Sin^2 θ]/ Cos^2 θ) dθ θ

= ∫([1 -Cos^2 θ]/ Cos^2 θ) dθ

= ∫[Sec^2 θ - 1]dθ

= ∫d[Tanθ] - ∫dθ

= Tanθ - θ + C. . . applying the limits 0.1 to 0.2 for θ,

= [0.20271 - 0.10033467] - 0.1

= 0.102375363 - 0.1

= 0.002375363. . . . ignoring C for the time being