Solution
= Solution
The original PDF specifies slope $\sqrt3$; the transcription's $\sqrt{-1}$ is erroneous. By part (a), $\cot(t/2)=\sqrt3$. Since $t/2\in(0,\pi)$ and <cotangent> is strictly decreasing there, the unique parameter value is $t=\pi/3$. Therefore
$$
\boxed{(x,y)=\left(a\left(\frac\pi3-\frac{\sqrt3}{2}\right),\frac a2\right).}
$$
The <tangent line> drawn in the preceding figure has the required positive slope.