Definition: An amphoteric oxide is an oxide that reacts with both acids and bases to form salt and water.
Example: Aluminium oxide (Al2O3)
When aluminium oxide reacts with hydrochloric acid, it behaves as a basic oxide:
Al2O3(s) + 6HCl(aq) → 2AlCl3(aq) + 3H2O(l)
Here, a salt (aluminium chloride) and water are formed.
When aluminium oxide reacts with sodium hydroxide, it behaves as an acidic oxide:
Al2O3(s) + 2NaOH(aq) + 3H2O(l) → 2Na[Al(OH)4](aq)
or simply:
Al2O3(s) + 2NaOH(aq) → 2NaAlO2(aq) + H2O(l)
In both reactions, a salt and water are produced.
Since aluminium oxide reacts with both acids and bases to form salt and water, it is classified as an amphoteric oxide.
General form: Al2O3 + HCl/NaOH → salt + H2O

In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$. 