Problem $1$ Using deflection methods, solve for the reactions of the statically indeterminate beam.

Note: there are $2$ redundants: $M_2$ and $R_2.$ Release the beam from these redundants, and use $2$ deflection conditions at right end of beam:

$y_1+y_2+y_3=0$ at $L$ and ${}_1+{}_2+{}_3=0,$ where the $1$ st term in each equation is is from the actual loading of released beam, the second term in each equation is from the reaction couple $M_2$ at right end, and the $3^{rd}$ term in each equation is from the reaction force $R_2$