Let two tangents are drawn to the curve $y^2-4(x+y)=3\sin \theta +4\cos \theta -15,x,y,\theta \in R$ from the origin whose slopes are $m_1,m_2$. If the vertex of the curve is at maximum distance from the origin, then the value of $\left|\frac{1}{m_1{m}_2}\right|$ is