  Planets may be rotationally flattened, and their oblateness thus provide
useful information on their formation and evolution. Here we develop a new
algorithm that can compute the transit light curve due to an oblate planet very
efficiently and use it to study the detectability of planet oblateness (and
spin obliquity) with the James Webb Space Telescope (JWST). Using the Jupiter
analog, Kepler-167e, as an example, we show that observations of a single
transit with JWST are able to detect a Saturn-like oblateness ($f=0.1$) with
high confidence, or set a stringent upper limit on the oblateness parameter, as
long as the planetary spin is slightly misaligned ($\gtrsim 20^\circ$) with
respect to its orbital direction. Based on known obliquity measurements and
theoretical arguments, it is reasonable to believe that this level of
misalignment may be common. We estimate the sensitivity limit of JWST in
oblateness detections and highlight the importance of better characterizations
of cold planets in planning future JWST transit observations. The potential to
detect rings, moons, and atmospheric species of the cold giants with JWST is
also discussed.
