Resolve the forces in the horizontal direction:

\(120 \cos 75^{\circ} = 150 - 100 - P \cos \theta\)

\(120 \cos 75^{\circ} = 50 - P \cos \theta\)

Resolve the forces in the vertical direction:

\(120 \sin 75^{\circ} = P \sin \theta\)

Using the Pythagorean identity for the resultant force:

\(P^2 = (P \cos \theta)^2 + (P \sin \theta)^2\)

\(P^2 = 14400 - 12000 \cos 75^{\circ} + 2500\)

Alternatively, use the tangent identity:

\(\tan \theta = \frac{120 \sin 75^{\circ}}{50 - 120 \cos 75^{\circ}}\)

Solving these equations gives:

\(P = 117\) N

\(\theta = 80.7^{\circ}\)