HKIMO 2020 THPT (Grades 10–12 shared) National Final (Heat) Set 01 Question 16

In right triangle $ABC$, $\angle B=90^\circ$ and $\angle C=15^\circ$. Point $D$ is on $BC$ and $AD=CD$. Given $\cos15^\circ=a\sqrt b+c\sqrt d$ with $a,b,c,d\gt 0$, find $a+b+c+d$.