Verified answer

There is no closed-form solution for this equation. It must be solved by numerical methods. Newton's method is probably a good one.

.. f(x) = x + cos(x) + (√3 - 1)/2 = 0

.. f'(x) = 1 - sin(x)

.. x(next) = x - f(x)/f'(x)

Starting at x=-1, the first few iterations are

-1,

-0.949132,

-0.948736,

-0.948736