If ∫( sin x)^(-11/2)( cos x)^(-5/2) d x= -p_1/q_1( cot x)^(9/2)-p_2/q_2( cot x)^(5/2)-p_3/q_3( cot x)^(1/2)+p_4/q_4( cot x)^(-3/2)+ C, where p_i and…

$$\begin{aligned} & \text { If } \int(\sin x)^{\frac{-11}{2}}(\cos x)^{\frac{-5}{2}} d x= \\ & -\frac{p_1}{q_1}(\cot x)^{\frac{9}{2}}-\frac{p_2}{q_2}(\cot x)^{\frac{5}{2}}-\frac{p_3}{q_3}(\cot x)^{\frac{1}{2}}+\frac{p_4}{q_4}(\cot x)^{\frac{-3}{2}}+\mathrm{C}, \text { where } p_i \text { and } q_i \end{aligned} $$ are positive integers with $\displaystyle \operatorname{gcd}\left(p_i, q_i\right)=1$ for $\displaystyle i=1,2,3,4$ and C is the constant of integration, then $\displaystyle \frac{15 p_1 p_2 p_3 p_4}{q_1 q_2 q_3 q_4}$ is equal to $\displaystyle \_\_\_\_$