The expression
= 2.5(10 cos 36 + 4 sin 35 - 3 cos 75)
= 5(10sin54+4sin35−3sin15)2
= 5(10(1+√54)+4((3√−√6+√232+(i32)(2√2−√3))−3√−√6+√232−(i32)(2√2−√3))−3(√3−12√2))2
Upper part is
5(10(1+√54)+4((3√−√6+√232+(i32)(2√2−√3))−3√−√6+√232−(i32)(2√2−√3))−3(√3−12√2))
I know this is complicated but it is completely real.
Source: http://intmstat.com/blog/2011/06/exact-values-sin-degrees.pdf
It has all exact values of sine of integers ranging from 1 - 90.