# Composition of two rotations in tikz

## Goal

Using tikz-3dplot, I would like to draw the great circle that delineates what would be the outline of the sphere of radius 1 as seen from the fixed viewpoint (in other words, the plane perpendicular to the vector describing the view direction) in order to avoid other great circles to give the impression that they "go out" of that sphere (purple outlines in the figure below, so which doesn't show any overlap with every of the other great circles).

### MWE

\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb}
\usepackage[english]{babel}
\usepackage{float}
\usepackage{tikz}
\usepackage{tikz-3dplot}
%%%%%%%%
\begin{document}
\pgfmathsetmacro{\rvec}{1}
\pgfmathsetmacro{\thetavec}{54}
\pgfmathsetmacro{\phivec}{54}
\pgfmathsetmacro{\view}{135}

\tdplotsetmaincoords{75}{\view}

\definecolor{darkgreen}{rgb}{0.1,0.9,0.1}

\begin{tikzpicture}[scale=5,tdplot_main_coords]
\coordinate (O) at (0,0,0);
% Axes
\draw[thick,->] (O) -- (2.0,0,0) node[anchor=north east]{$X$};
\draw[thick,->] (O) -- (0,2.0,0) node[anchor=north west]{$Y$};
\draw[thick,->] (O) -- (0,0,1.4) node[anchor=south]{$Z$};

% Great circle in the OXZ plane
\tdplotsetthetaplanecoords{0}
\tdplotdrawarc[tdplot_rotated_coords]{(O)}{\rvec}{0}{180}{}{}
\tdplotdrawarc[tdplot_rotated_coords,loosely dashed,gray]{(O)}{\rvec}
{180}{360}{}{}

% Great circle in the OYZ plane
\tdplotsetthetaplanecoords{90}
\tdplotdrawarc[tdplot_rotated_coords]{(O)}{\rvec}{0}{180}{}{}
\tdplotdrawarc[tdplot_rotated_coords,losely dashed,gray]{(O)}{\rvec}
{180}{360}{}{}

% Great circle in the OXY plane
\tdplotdrawarc[blue]{(O)}{\rvec}{-55}{125}{}{}
\tdplotdrawarc[loosely dashed,blue]{(O)}{\rvec}{125}{305}{}{}

%% Testing great circles
% Rotated Great circle around Z-axis, this is the first wanted rotation
% to bring it in the original, non rotated "O-Y_ori-Z" plane.
\tdplotsetthetaplanecoords{\view}
\tdplotdrawarc[tdplot_rotated_coords,cyan]{(O)}{\rvec}{0}{360}{}{}

% Rotated big circle around Y-axis, this second rotation should be applied
% just after the previous one, i.e. on the great circle colored in cyan.
% How to do that ?
\tdplotsetrotatedthetaplanecoords{15}
\tdplotdrawarc[tdplot_rotated_coords,darkgreen]{(O)}{\rvec}{0}{360}{}{}

\end{tikzpicture}
\end{document}



Result of the current code:

What I would like is to get the result of the composition of the first, then the second rotation (in that order) in the Testing part but I don't know how to tell that to tikz.

Adding this to the tikzpicture solved the described problem:
\tdplotsetrotatedcoords{\azimuth-90}{75}{0}

The magical appears by using the \tdplotsetrotatedcoords function: