The latitude and longitude of a point P in the Northern Hemisphere are related to spherical coordinates ρ, θ, Φ as follows. We take the origin to be the center of the earth and the positive z-axis to pass through the North Pole. The positive x-axis passes through the point where the prime meridian (the meridian through Greenwich, England) intersects the equator. Then the latitude of P is α = 90° − Φ° and the longitude is β = 360° − θ°. Find the great-circle distance from Los Angeles (lat. 34.06° N, long. 118.25° W) to Montréal (lat. 45.50° N, long. 73.60° W). Take the radius of the earth to be 3960 mi. (A great circle is the circle of intersection of a sphere and a plane through the center of the sphere.)