Straight Lines And Pair Of Straight Lines

Consider three points \(P = ( - \sin (\beta - \alpha ), - cos\beta ),Q = (cos(\beta - \alpha ),\sin \beta )\) and \(R = (\cos (\beta - \alpha + \theta ),\sin (\beta - \theta ))\) where \(0 < \alpha ,\beta ,\theta < {\pi \over 4}\). Then :