trigonometrical range...quite interesting

Geometry Level 4

If the range of the expression for θnπ,nIntegers\theta\neq n\pi,n \in Integers cosec2θ+cotθcosec2θcotθ\dfrac{cosec^2\theta+cot\theta}{cosec^2\theta-cot\theta} is [a,b]\large [a,b].

Find the value of ba\dfrac{b}{a}


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