Gauss's Hypergeometric Theorem/Corollary 2

Corollary to Gauss's Hypergeometric Theorem
Let $\map \Re {a - 1} < 0$.

Then:


 * $\ds \dfrac 1 a + \dfrac {a } {\paren {a + 1} 1!} + \dfrac {a \paren {a + 1} } {\paren {a + 2} 2!} + \dfrac {a \paren {a + 1} \paren {a + 2} } {\paren {a + 3} 3!} + \cdots = \dfrac {\pi} {\map \sin {\pi a } } $

Proof
Set $c - 1 = a$ in Corollary 1:

Before substitution:

After substitution: