How do we show on a picture that a solid angle equals to this equation i found on a Wikipedia:
\begin{align} \Omega =\!\!\!\int\limits_{\vartheta =0}^{\pi}\int\limits_{\varphi=0}^{2\pi}\underbrace{\sin\vartheta\, \textrm{d}\vartheta\, \textrm{d}\varphi}_{\textrm{d}\Omega} \end{align}
Draw a "square" on a sphere from latitude $\frac \pi 2- \vartheta$ to $\frac \pi 2- \vartheta + d \vartheta$ and longitude $\varphi$ to $\varphi + d\varphi$. Note that the linear distance along the line of latitude is $\sin \vartheta d\varphi$ and the distance along the line of longitude is $d\vartheta$