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From an external point \( P \), pair of tangent lines are
\( \mathrm{P} \) drawn to the parabola, \( y^{2}=4 x \). If \( \theta_{1} \) and \( \theta_{2} \) are the

W. inclinations of these tangents with the axis of \( x \) such that, \( \theta_{1}+\theta_{2}=\frac{\pi}{4} \), then the locus of \( P \) is:
(1) \( x-y+1=0 \)
(2) \( x+y-1=0 \)
(3) \( x-y-1=0 \)
(4) \( x+y+1=0 \)
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