As other reviewers have noted, this card pairs beautifully with Alyssa Graham. Basically, Alyssa lets you look at the top encounter card for free, but makes you pay a hefty price -- doom -- to get rid of it. Split the Angle makes you pay to peek -- an action -- but then discard what you saw mostly for free. Put the two together, and it's ALL free.
Commenters, however, have done what commenters do, and raised annoyingly rational objections. They point out that you only get one StA, so you might never find it at all, and if you do, there's no guarantee Alyssa is in play, etc. etc., doom and gloom. Unfortunately, they are right...
I think, in the end, StA takes a sweeping deckbuilding commitment to make it reliably good. Step one is including 2 copies of Alyssa Graham. As others have noted, you'll probably want to upgrade into level 3 Scrying. Scrying is especially handy in solo, because it gives you multiples turns of information about the encounter deck in a single use. Say you're solo-ing away, and in the tea leaves you find a pair of ancient evils and something relatively harmless. You can arrange them into an Evils-Meh-Evils sandwich; and use StA two turns in a row to discard the two slices of death-bread, drawing only the mild Meh in between (and something random) -- all for no actions at all. Of course, the downside here is that you are now using both your arcane slots on encounter-deck mining...
As long as you're investing in all these cards that let you burn through or optimally order the encounter deck, you may as well toss in Stargazing (you are an astronomer, after all...). You're much more likely to actually draw the The Stars Are Right if you can dig for it with Alyssa/StA/Scrying.
With 2 copies of Alyssa and 2 copies of level 3 Scrying, the odds are now pretty good that if you do manage to draw StA, you'll have something to pair it with. If you are absolutely determined to make this combination happen, Word of Command can help you find StA or Scrying, and Calling in Favors can help you track down a shy Alyssa.
By now, we're talking about quite a commitment! Is it worth it? Strategically, maybe not, but it might make for a fun thematic build. A prescient astronomer with occult leanings reading doom in the night skies -- and then somehow averting it by means of dubious geometry or an eldritch astrolabe -- that sounds pretty Arkham-y to me.
