Is there a space in which the $\vec a$ in $\sin(a_1\cdot x)+\sin(a_2\cdot x)$ is linear?

Question

I have equations of the form $\sin(a_1\cdot x)+\sin(a_2\cdot x)=y$ (actually more complicated, but that's the general essence). I want to solve for $\vec a$ using linear regression instead of non-linear regression / optimization / etc. Is there perhaps some transform that would give me something like $$T[\sin(a_1\cdot x)+\sin(a_2\cdot x)] = a_1\cdot x + a_2\cdot x = T[y]$$ that I could then use linear regression to solve? I know of existing methods like the Lomb-Scargle Periodogram etc but I am trying to understand whether there is a separate route.