Identify the end product (Z) in the sequence of the following reactions:
The sequence of reactions starts with a base-promoted elimination, followed by a rearrangement and a substitution to finally produce the ester \(O_2CCH_3\) as the end product.
The reagents and conditions (X) required for the following conversion
\[ \sin^{-1} x - \cos^{-1} 2x = \sin^{-1} \left(\frac{\sqrt{3}}{2}\right) - \cos^{-1} \left(\frac{\sqrt{3}}{2}\right) \]
Then, \[ \tan^{-1} x + \tan^{-1} \left(\frac{x}{x+1}\right) = ? \]