Define the sequence a_{1}, a_{2}, a_{3}, \ldots by a_{n}=\sum_{k=1}^{n} \sin (k), where k represents radian measure. Find the index of the \text { 100th } term for which a_{n}<0.
Define the sequence a_{1}, a_{2}, a_{3}, \ldots by a_{n}=\sum_{k=1}^{n} \sin (k), where k represents radian measure. Find the index of the \text { 100th } term for which a_{n}<0.