Question 171
Let $ABC$ be an acute triangle and let $I$ be the incentre of the triangle $ABC$. The lines $AI$ and $BI$ meet the circumcircle of the triangle $ABC$ again at $A_1$ and $B_1$. The segments $A_1B_1$ and $CI$ meet at $C_1$. Let $S$ be the circumcentre of the triangle $IA_1C_1$. The lines $SC_1$ and $BI$ meet the segment $AC$ at $D$ and $E$. Find the angles of the triangle $ABC$ if $|CD| = |DE|$ and $\angle CBA = 2\angle ACB$.