How can I solve a difference of inverse sines? I'm trying to solve the equation
$$\arcsin(\lambda_1 / d) - \arcsin(\lambda_2 / d) = \pi / 6$$
for $d$, where $\lambda_1$ and $\lambda_2$ are known.
I don't really know where to start here.
I don't know any identities for inverse trigonometric functions akin to the ones like $\sin(u + v) = \sin u \cos v + \cos u \sin v$.
I see via Wikipedia that these have complex logarithmic forms, but I don't see how that might help (and I don't know any complex analysis).
Mathematica and WolframAlpha each give me a closed-form expression, but refuse to show how:

What's the best/cleanest way to go about solving this?

Note that if $\sin x=y$, then since
$$\sin^2 x+\cos^2 x=1$$
we have that $\cos x=\pm \sqrt{1-y^2}$. Use this together with the sum formula.
