f(x):=asin(2*x)+asin(12/13)=acos(33/65); /* problem */;

g(x):=asin(2*x)+asin(12/13)=asin(56/65); /* diagram */;

h(x):= asin(2*x)=asin(56/65)-asin(12/13); /* algebra */;

identity(a,b):= asin(a)-asin(b)=asin(a*sqrt(1-b^2)-b*sqrt(1-a^2)); /* identity */;

result:identity(56/65,12/13); /* apply identity */;

lhs(h(x))=rhs(result); /* apply result */;

is(equal(asin(-x),-asin(x))); /* check if sign can move inside */;

u(x):=asin(2*x)=asin(-116/845); /* algebra */;

sin(u(x)); /* apply inverse operator, beautiful */;

first(solve(sin(u(x)))) /* final algebra */;