$(3)$ Consider a long slender beam with a length $L,$ constant Young's modulus $E,$ and constant second order moments of area I. The beam is simply supported at its left edge and clamped at its right edge at an angle of $3.$ The forced rotation at the right edge causes the beam to deflect $($dashed line$)$ and induces internal stresses in the beam.

$($a$)$ Is this problem statically determinate? Explain briefly.

$($b$)$ Determine the slope of the beam at its left edge.

$($c$)$ Determine the reaction force at the left edge of the beam.