Among all triangles $ABC,$ find the maximum value of $\sin A + \sin B \sin C.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Among all triangles $ABC,$ find the maximum value of $\sin A + \sin B \sin C.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1 + \sqrt{5}}{2}
Among all triangles $ABC,$ find the maximum value of $\sin A + \sin B \sin C.$
train