The angle \theta_1θ
1

theta, start subscript, 1, end subscript is located in Quadrant \text{III}IIIstart text, I, I, I, end text, and \cos(\theta_1)=-\dfrac{13}{30}cos(θ
1

)=−
30
13

cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 13, divided by, 30, end fraction .
What is the value of \sin(\theta_1)sin(θ
1

)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Express your answer exactly.