||\alpha'||^2 = I(\alpha',\alpha') =
\left(
\begin{array}{cc}
-\rho \sin t & \rho \cos t
\end{array}\right)
 \left(
\begin{array}{cc}
 \frac{1}{\rho^2 \sin^2 t} & 0  \\
 0 & \frac{1}{\rho^2 \sin^2 t} 
\end{array}\right)
\left(
\begin{array}{cc}
-\rho \sin t    \\
\rho \cos t
\end{array}\right)
 = \frac{1}{\sin^2 t}