Two cautions should be noted about (4.8), and other formulas similar to it that may be encountered.
1) At higher latitudes in summer, Ѳ noticeably exceeds 90⁰ in early to mid morning and from mid to late evening, when the sun rises from or falls to the observer’s horizon (i.e. cos Ѳ negative). When this happens for instance in the northern hemisphere, sunshine is on the north side of buildings and on the rear side of a fixed south-facing collector, not the front.