Simplify and evaluate the following expression without using logarithmic tables or calculators:
a. (a) Rewrite cos780∘ as the cosine of an angle in the interval [0∘,360∘).
b. (b) Express sin(−300∘) as the sine of an angle in the interval [0∘,360∘).
c. (c) Further rewrite each term obtained in parts (a) and (b) entirely in terms of sine of acute angles using a suitable co-function relation, and hence find the exact value of cos780∘+sin(−300∘).
d. (d) Verify your answer by numerical substitution of the standard exact values involved.