Definite double integral in Mathematica

I am a beginner in Mathematica. I want to perform the following definite double integral equation in Mathematica and want to compare the solution with mine.

$$A_{P-A} = R^2\int_{\theta=\frac\pi2-\beta}^{\alpha_\text{eq}}\int_{\phi=\arcsin(1/\tan\beta\tan\theta)}^{\pi-\arcsin(1/\tan\beta\tan\theta)}\sin\theta\mathrm{d}\theta\mathrm{d}\phi$$

$$A_{P-A} = \pi R^2(1-\cos\alpha_\text{eq})+2R^2\left[\cos\alpha_\text{eq}\arcsin(\cot\beta\cot\alpha_\text{eq})-\arctan\frac{\cos\beta}{\sqrt{\sin^2\beta-\cos^2\alpha_\text{eq}}}\right]$$

I wrote the command by following Mathematica tutorial for the integral and it is not showing any result and keep running for over 2 hours. Am I making any mistakes?

R^2 Integrate[  Sin[\[Theta]], {\[Theta], (Pi/2), \[Alpha] }, {\[Phi],    ArcSin[1/(Tan[\[Theta]]*Tan[\[Beta]])],    Pi - ArcSin[1/(Tan[\[Theta]]*Tan[\[Beta]])]}]