Answer
The tangential acceleration is $~g~sin~\theta$
Work Step by Step
The tension in the string is perpendicular to the direction of motion, so it does not affect the tangential acceleration. The component of the gravitational force directed parallel to the direction of motion provides the force for the tangential acceleration:
$mg~sin~\theta = m~a_t$
$a_t = g~sin~\theta$
The tangential acceleration is $~g~sin~\theta$.
