Complete the identity:
see attached photo.

2csc^2(Θ) - 1

Explanation:
The given is:
(1 + cos^2(Θ)) / sin^2(Θ)
Now,
sin^2 (Θ) + cos^2(Θ) = 1
This means that:
cos^2(Θ) = 1 -  sin^2 (Θ) > I

Substitute with I in the given equation, this will lead to:
(1+1-sin^2 (Θ) ) / sin^2(Θ)
(2-sin^2 (Θ) ) / sin^2(Θ)

This expression can be written as:
[2/sin^2(Θ)] - [sin^2 (Θ) / sin^2(Θ)]

This is equivalent to:
2csc^2(Θ) - 1

Hope this helps :)

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