  We study the Page curve and the information paradox for the BTZ black hole
coupled to two thermal baths by applying the island paradigm. We prove that as
the island locates outside the event horizon, the entanglement entropy of
Hawking radiation for finite temperature black holes obeys the Page curve.
However, for extremal rotating black holes, the Page time and the scrambling
time become divergent. To avoid the ill-defined of the Page time, we consider
the contribution of superradiance, which is a process that can extract
rotational energy from black holes. The superradiance continues in a period
much shorter than the Page time when the central charge $c$ is not too large.
In this process, the Page time, the scrambling time and the black hole thermal
entropy all decrease. Whenever the superradiance finishes, the black hole turn
out to be a neutral black hole and the Hawking radiation dominates. The Page
curve can then be well reproduced.
