Prove that this relationship is true (Image Attached)

From the picture, we can see that
[tex]\sin\theta=\dfrac HB\implies\dfrac{\sin\theta}C=\dfrac H{BC}[/tex]
[tex]\sin\beta=\dfrac HC\implies\dfrac{\sin\beta}B=\dfrac H{BC}[/tex]
which means
[tex]\dfrac{\sin\theta}C=\dfrac{\sin\beta}B[/tex]