With all of this being said, if you're eager to start with Spivak, there's no problem in just starting and seeing how successful you are on the exercises in the first few chapters.

Algebra | SpringerLink Algebra | SpringerLink

Langlands, R. P. (1976). " SL 2(R), by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (5): 688–691. doi: 10.1090/s0002-9904-1976-14109-2. Lang, Serge (1995). Introduction to Diophantine approximations (Second edition of 1966 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-4220-8. ISBN 0-387-94456-7. MR 1348400.

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Lang, Serge (1990). Cyclotomic fields I and II. Graduate Texts in Mathematics. Vol.121. With an appendix by Karl Rubin (Combined second edition of 1978/1980 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-0987-4. ISBN 0-387-96671-4. MR 1029028. Meacham, R. C. (1966-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 39 (2): 124. doi: 10.2307/2688730. JSTOR 2688730. Niven, Ivan (1970-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 43 (5): 277–278. doi: 10.2307/2688750. JSTOR 2688750.

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Jorgenson, Jay; Lang, Serge (2008). The heat kernel and theta inversion on SL 2(C). Springer Monographs in Mathematics. New York: Springer. doi: 10.1007/978-0-387-38032-2. ISBN 978-0-387-38031-5. MR 2449649. Jorgenson, Jay; Lang, Serge (1993). Basic Analysis of Regularized Series and Products. Lecture Notes in Mathematics. Vol.1564. Berlin: Springer-Verlag. doi: 10.1007/BFb0077194. ISBN 3-540-57488-3. MR 1284924. Lang, Serge (1983). Complex multiplication. Grundlehren der mathematischen Wissenschaften. Vol.255. New York: Springer-Verlag. doi: 10.1007/978-1-4612-5485-0. ISBN 0-387-90786-6. MR 0713612. Part (2) is important, and I agree that Lang's book is short on this topic. But the trigonometry and complex number chapters of Parsonson's Pure Mathematics 1 and 2 (which I mentioned to you previously) ought to be quite enough for this. It's not necessary that this be taken beyond the level of Lang before you study calculus.Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Vol.211 (Revised third edition of 1965 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4613-0041-0. ISBN 0-387-95385-X. MR 1878556.