(doCarmo 2.5-2)Let (,)=(sincos,sinsin,cos) be parametrization of the sphere $^2$ . Let be the plane =cot , 0<< and be the acute angle which the curve $∩^2$ makes with the semimeridian $$=$_0$ . Compute cos .
I've followed hints from posts on the same question. But still not sure how to proceed after having $cot\alpha=tan\theta cot\alpha$ and $x_{\theta}$, $x_{\phi}$. I guess I'm supposed to find $\theta'$ and $\phi '$ but I'm not sure how.