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If \( \theta_{1} \& \theta_{2} \) are the parameters of the extremities of a chord through \( (a e, 0) \) of a hyperbola
\[
\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \text {, then show that } \tan \frac{\theta}{2} \cdot \tan \frac{\theta}{2}+\frac{e-1}{e+1}=0 \text {. }
\]
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