Consider the two complex numbers \( z \) and \( w \), such that \( ...

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Consider the two complex numbers \( z \) and \( w \), such that \( w=\frac{z-1}{z+2}=a+i b \), where \( a, b \in R \) and \( i=\sqrt{-1} \).
\( \mathrm{P} \) Which of the following is the value of \( -\frac{b}{a} \), whenever it

W exists?
(a) \( 3 \tan \left(\frac{\theta}{2}\right) \)
(b) \( \frac{1}{3} \tan \left(\frac{\theta}{2}\right) \)
(c) \( -\frac{1}{3} \cot \theta \)
(d) \( 3 \cot \frac{\theta}{2} \)
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