Consider a vector in two dimensional space:
\overrightarrow{v} = \widehat{i}
starting at r = 1, \theta = 0, and moving around the unit circle with constant r = 1, but varying \theta. the assumption is that the vector itself should not vary (i. e. the semicolon derivatives should be zero around the curve).
write (and solve if possible) a differential equation describing the changes in the components of \overrightarrow{v} as you parallel-transport it around the unit circle.