= Solution
Initialize three <qubits> in $|000\rangle$. Apply a <Hadamard gate> on the first, then <controlled-NOT gates> $1\to2$ and $1\to3$:
$$
|000\rangle\longmapsto\frac{|000\rangle+|100\rangle}{\sqrt2}
\longmapsto\frac{|000\rangle+|111\rangle}{\sqrt2}.
$$
Apply the <T gate> twice to the first <qubit>. Because $T^2=\operatorname{diag}(1,i)$, the resulting <GHZ state> with the specified <relative quantum phase> is
$$
\boxed{T_1^2\operatorname{CNOT}_{1\to3}\operatorname{CNOT}_{1\to2}H_1|000\rangle
=\frac{|000\rangle+i|111\rangle}{\sqrt2}.}
$$
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