Prove the Identity: ( theta + 2theta * theta)/( theta) = theta

Let's prove the first identity.

1) Prove the Identity: $\frac{\cos \theta + \sin 2\theta \cdot \sec \theta}{\csc \theta} = \tan \theta$

Step 1: Rewrite the left-hand side (LHS) in terms of $\sin \theta$ and $\cos \theta$.
We use the identities:
$\sin 2\theta = 2 \sin \theta \cos \theta$
$\sec \theta = \frac{1}{\cos \theta}$
$\csc \theta = \frac{1}{\sin \theta}$

Substitute these into the LHS:

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