= Solution
Substitute $R=r^{\pi/\alpha}$ from part (a) into part (c). The <Brownian wedge-exit probability> is
$$
\boxed{\mathbb P_1\{B[0,T(r)]\subset W_\alpha\}
=\frac4\pi\arctan\!\left(r^{-\pi/\alpha}\right)
=\frac2\pi\arctan\!\left(\frac{2r^{\pi/\alpha}}{r^{2\pi/\alpha}-1}\right).}
$$
It tends to $1$ as $r\downarrow1$, and is asymptotic to $(4/\pi)r^{-\pi/\alpha}$ as $r\to\infty$. The exponent reflects how the <conformal map> stretches wedge angles; wider wedges give slower decay.
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