Compute Solid Angle of Cone: θ | Hi Everyone

[azerty12]

Hi everyone

I'd like to compute the solide angle defined by a cone whose angle θ is known.
I tried with the definition but I probably mistook since it lead me to compute an integral worth...0.
I then tried with a rule of three, but the result I get is clearly wrong too.

Could you explain me how to proceed?

 

[emgram769]

Try this:
$\int_0^{2\pi}\,\int_0^\theta\,sin\theta\,\mathrm{d}\theta\,\mathrm{d}\phi$

for a cone with apex angle 2theta

via wikipedia

 

[azerty12]

Thank you emgram769: In fact that's almost what I tried to do but I took the second integral with -theta instead of 0 (and we should take 0 because phi is integrated over 2Pi)