If 7sin² θ + 3cos² θ = 4, 0 <  θ < 90°, then the value of \(\frac{tan^2 2 θ - sin^2  θ}{cot θ + cosec2 θ}\)?

\(\frac{11\sqrt {3 }}{20}\)

7sin² θ + 3cos² θ = 4

 θ = 30° satisfies the equation

⇒ \(\frac{tan^2 2 θ - sin^2 θ}{cot  θ + cosec2 θ}\) = \(\frac{tan^2 60° - sin^2 30°}{cot 30° + cosec 60°}\)

= \(\frac{3 -\frac{1}{4}}{\sqrt {3} + \frac{2}{\sqrt {3}}}\)

= \(\frac{\frac{11}{4}}{\frac{5}{\sqrt {3}}}\)

= \(\frac{11 \sqrt {3}}{20}\)