Check out the attached image below for the steps on how to do this derivation.
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Some notes:
For line 2, I used the identity [tex]\sec^2\theta = \tan^2\theta+1[/tex]
For line 7, I applied the reciprocal to both sides.
For line 8, I used the identity [tex]\cot\theta = \frac{1}{\tan\theta}[/tex]
For line 9, I used the identty [tex]\cot^2\theta = \csc^2\theta - 1[/tex] which is a rearrangement of [tex]\cot^2\theta + 1 = \csc^2\theta[/tex]
For lines 1 through 6, I'm isolating tan^2, so that I can later transform that into cot^2, which leads to csc^2. All of this is done through the identities mentioned above.
