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This solution comes from Andrei from Tudor Vianu National College, Bucharest, Romania.
To solve this problem I see that the data are given in spherical coordinates, but I need to work in Cartesian coordinates.
I choose the Cartesian system of coordinates with the origin at the centre of the Earth, with the $xy$ plane  the equatorial plane, and the $z$ axis directed towards the North Pole. The spherical system of coordinates has the origin at the same point as the Cartesian one, i.e. at the centre of the Earth. Let the angle $p$ measure the latitude (0 at the equator and $\pi/2$ at the North
Pole), i.e. it is the angle between the position vector of the current point $P$ and the plane $xOy$. Let the angle $q$ measure the longitude (in respect to the axis $Ox$), i.e. it is the angle between the projection of the position vector of point $P$ on the plane $xOy$ and the $x$ axis. So the 3D coordinates in terms of the angles of latitude and longitude are: $$x = R \cos p \cos q, y = R \cos
p \sin q, z = R \sin p.$$
